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Algebraic structure
especially in the field of algebra, a polynomial ring or polynomial algebra is a ring formed from the set of polynomials in one or more indeterminates (traditionally
Polynomial_ring
Type of mathematical expression
approximate other functions. In advanced mathematics, polynomials are used to construct polynomial rings and algebraic varieties, which are central concepts
Polynomial
Mathematical construct in computer algebra
Gröbner basis is a particular kind of generating set of an ideal in a polynomial ring K [ x 1 , … , x n ] {\displaystyle K[x_{1},\ldots ,x_{n}]} over a field
Gröbner_basis
Free object in the category of associative algebras
known as ring theory, a free algebra is the noncommutative analogue of a polynomial ring since its elements may be described as "polynomials" with non-commuting
Free_algebra
Algebraic structure with addition and multiplication
also be non-numerical objects such as polynomials, square matrices, functions, and power series. More formally, a ring is a set that is endowed with two binary
Ring_(mathematics)
In ring theory, a branch of mathematics, a ring R is a polynomial identity ring if there is, for some N > 0, an element P ≠ 0 of the free algebra, Z⟨X1
Polynomial_identity_ring
Algebraic structure
mathematics, the ring of polynomial functions on a vector space V over a field k gives a coordinate-free analog of a polynomial ring. It is denoted by
Ring_of_polynomial_functions
Tool in mathematical dimension theory
ideal of a multivariate polynomial ring, graded by the total degree. The quotient by an ideal of a multivariate polynomial ring, filtered by the total
Hilbert series and Hilbert polynomial
Hilbert_series_and_Hilbert_polynomial
Greatest common divisor of polynomials
GCD or gcd) of two polynomials is a polynomial, of the highest possible degree, which is a factor of both the two original polynomials. This concept is
Polynomial greatest common divisor
Polynomial_greatest_common_divisor
Type of commutative ring in mathematics
theorem for polynomial rings, and for Irvin Cohen (1946), who proved the unmixedness theorem for formal power series rings. All Cohen–Macaulay rings have the
Cohen–Macaulay_ring
content by a unit of the ring of the coefficients (and the multiplication of the primitive part by the inverse of the unit). A polynomial is primitive if its
Primitive_part_and_content
Branch of algebra that studies commutative rings
commutative algebra. Prominent examples of commutative rings include polynomial rings; rings of algebraic integers, including the ordinary integers Z
Commutative_algebra
Polynomial without nontrivial factorization
ring to which the coefficients of the polynomial and its possible factors are supposed to belong. For example, the polynomial x2 − 2 is a polynomial with
Irreducible_polynomial
About products of primitive polynomials
Gauss, is a theorem about polynomials over the integers, or, more generally, over a unique factorization domain (that is, a ring that has a unique factorization
Gauss's_lemma_(polynomials)
Set of a ring's prime ideals
is the univariate polynomial ring. The kernel of this homomorphism is the principal ideal generated by the minimal polynomial m T ( x ) {\displaystyle
Spectrum_of_a_ring
Concept in abstract algebra
E/F} . The minimal polynomial of an element, if it exists, is a member of F [ x ] {\displaystyle F[x]} , the ring of polynomials in the variable x {\displaystyle
Minimal polynomial (field theory)
Minimal_polynomial_(field_theory)
Topology on prime ideals and algebraic varieties
the polynomial ring over a field k {\displaystyle k} : such a polynomial ring is known to be a principal ideal domain and the irreducible polynomials are
Zariski_topology
Mathematical function
elementary symmetric polynomials are one type of basic building block for symmetric polynomials, in the sense that any symmetric polynomial can be expressed
Elementary symmetric polynomial
Elementary_symmetric_polynomial
Polynomial with negative exponents
polynomials in X {\displaystyle X} form a ring denoted F [ X , X − 1 ] {\displaystyle \mathbb {F} [X,X^{-1}]} . They differ from ordinary polynomials
Laurent_polynomial
Polynomial with 1 as leading coefficient
In algebra, a monic polynomial is a non-zero univariate polynomial (that is, a polynomial in a single variable) in which the leading coefficient (the
Monic_polynomial
Mathematical concept
In mathematics, the degree of a polynomial is the highest of the degrees of the polynomial's monomials (individual terms) with non-zero coefficients. The
Degree_of_a_polynomial
Polynomial whose nonzero terms all have the same degree
coordinates over any basis. A polynomial of degree 0 is always homogeneous; it is simply an element of the field or ring of the coefficients, usually called
Homogeneous_polynomial
"Smallest" commutative algebra that contains a vector space
algebra S(V) can be identified, through a canonical isomorphism, to the polynomial ring K[B], where the elements of B are considered as indeterminates. Therefore
Symmetric_algebra
Algebraic variety defined within an affine space
zeros over an algebraically closed field k of some family of polynomials in the polynomial ring k [ x 1 , … , x n ] . {\displaystyle k[x_{1},\ldots ,x_{n}]
Affine_variety
Vector space equipped with a bilinear product
group multiplication. the commutative algebra K[x] of all polynomials over K (see polynomial ring). algebras of functions, such as the R-algebra of all real-valued
Algebra_over_a_field
finite groups states that the ring of invariants of a finite group acting on a complex vector space is a polynomial ring if and only if the group is generated
Chevalley–Shephard–Todd theorem
Chevalley–Shephard–Todd_theorem
Computational problem possibly useful for post-quantum cryptography
learning with errors over rings and is simply the larger learning with errors (LWE) problem specialized to polynomial rings over finite fields. Because
Ring_learning_with_errors
X1, X2, ..., XN] is the polynomial ring in N + 1 variables Xi. The polynomial ring is therefore the homogeneous coordinate ring of the projective space
Homogeneous_coordinate_ring
the ring of symmetric functions is a specific limit of the rings of symmetric polynomials in n indeterminates, as n goes to infinity. This ring serves
Ring_of_symmetric_functions
Polynomial that permutes a ring
mathematics, a permutation polynomial (for a given ring) is a polynomial that acts as a permutation of the elements of the ring, i.e. the map x ↦ g ( x )
Permutation_polynomial
In mathematics, dimension of a ring
variety: the dimension of the affine variety defined by an ideal I in a polynomial ring R is the Krull dimension of R/I. A field k has Krull dimension 0; more
Krull_dimension
Generalization of vector spaces from fields to rings
spaces (vector spaces over K). If K is a field, and K[x] a univariate polynomial ring, then a K[x]-module M is a K-module with an additional action of x
Module_(mathematics)
Boolean polynomials as sums of monomials
algebra. Formulas written in ANF are also known as ring sum normal form (RSNF or RNF), Zhegalkin polynomials (Russian: полиномы Жегалкина), or Positive Polarity
Algebraic_normal_form
Branch of algebra
for its applications, such as homological properties and polynomial identities. Commutative rings are much better understood than noncommutative ones. Algebraic
Ring_theory
Computational method
mathematics and computer algebra, factorization of polynomials or polynomial factorization expresses a polynomial with coefficients in a given field or in the
Factorization_of_polynomials
Mathematical concept in polynomial theory
resultant of two polynomials is a polynomial expression of their coefficients that is equal to zero if and only if the polynomials have a common root
Resultant
Ideal in a ring which has properties similar to prime elements
if an element in a polynomial ring is irreducible. If R denotes the ring C [ X , Y ] {\displaystyle \mathbb {C} [X,Y]} of polynomials in two variables with
Prime_ideal
Mathematical structure in abstract algebra
ring K and its polynomial ring K[x]: the quotient by x = 0 restores K. In Hecke algebra, an involution is important to the Kazhdan–Lusztig polynomial
*-algebra
Algebraic structure
commutative ring. The rational, real and complex numbers form fields. If R {\displaystyle R} is a given commutative ring, then the set of all polynomials in the
Commutative_ring
On polynomial rings over fields
Hilbert's syzygy theorem is one of the three fundamental theorems about polynomial rings over fields, first proved by David Hilbert in 1890, that were introduced
Hilbert's_syzygy_theorem
Point where function's value is zero
algebraic set is the intersection of the zero sets of several polynomials, in a polynomial ring k [ x 1 , … , x n ] {\displaystyle k\left[x_{1},\ldots ,x_{n}\right]}
Zero_of_a_function
Mathematical object studied in the field of algebraic geometry
Nullstellensatz provides a fundamental correspondence between ideals of polynomial rings and algebraic sets. Using the Nullstellensatz and related results,
Algebraic_variety
Direct summand of a free module (mathematics)
a principal ideal domain such as the integers, or a (multivariate) polynomial ring over a field (this is the Quillen–Suslin theorem). Projective modules
Projective_module
Algebraic structure
{\displaystyle S=k[x_{1},\dots ,x_{n}]} a polynomial ring over it. If f {\displaystyle f} is a square-free nonconstant polynomial in S {\displaystyle S} , then S
Integrally_closed_domain
Algebraic construction
{\displaystyle K} ) is the ring of all algebraic integers contained in K {\displaystyle K} . An algebraic integer is a root of a monic polynomial with integer coefficients:
Ring_of_integers
field. Over an infinite field, the twisted polynomial ring is isomorphic to the ring of additive polynomials, but where multiplication on the latter is
Twisted_polynomial_ring
Mathematical operation
mathematics, the formal derivative is an operation on elements of a polynomial ring or a ring of formal power series that mimics the form of the derivative
Formal_derivative
Mathematical ring with well-behaved ideals
particular the ring of integers, polynomial rings, and rings of algebraic integers in number fields), and many general theorems on rings rely heavily on
Noetherian_ring
Polynomial ideals are finitely generated
every ideal of a polynomial ring over a field has a finite generating set (a finite basis in Hilbert's terminology). In modern algebra, rings whose ideals
Hilbert's_basis_theorem
Structure-preserving function between two rings
i for the variable X in the polynomial p) is a surjective ring homomorphism. The kernel of f consists of all polynomials in R[X] that are divisible by
Ring_homomorphism
Relation between algebraic varieties and polynomial ideals
numbers). Consider the polynomial ring k [ X 1 , … , X n ] {\displaystyle k[X_{1},\ldots ,X_{n}]} and let J be an ideal in this ring. The algebraic set V
Hilbert's_Nullstellensatz
Expression in commutative algebra
homogeneous symmetric polynomials are a specific kind of symmetric polynomials. Every symmetric polynomial can be expressed as a polynomial expression in complete
Complete homogeneous symmetric polynomial
Complete_homogeneous_symmetric_polynomial
Basis of polynomials consisting of monomials
mathematics the monomial basis of a polynomial ring is its basis (as a vector space or free module over the field or ring of coefficients) that consists of
Monomial_basis
Real numbers adjoined with a nil-squaring element
the algebra of dual numbers is often defined as the quotient of a polynomial ring over the real numbers ( R ) {\displaystyle (\mathbb {R} )} by the principal
Dual_number
Typically linear operator defined in terms of differentiation of functions
shift theorem. If R is a ring, let R ⟨ D , X ⟩ {\displaystyle R\langle D,X\rangle } be the non-commutative polynomial ring over R in the variables D
Differential_operator
Commutative algebra theorem
the relationship between free modules and projective modules over polynomial rings. In the geometric setting it is a statement about the triviality of
Quillen–Suslin_theorem
Category whose objects are rings and whose morphisms are ring homomorphisms
of Ring. The free commutative ring on a set of generators E is the polynomial ring Z[E] whose variables are taken from E. This gives a left adjoint functor
Category_of_rings
Pair of polynomial sequences
The Chebyshev polynomials are two sequences of orthogonal polynomials related to the cosine and sine functions, notated as T n ( x ) {\displaystyle T_{n}(x)}
Chebyshev_polynomials
quotient ring of the free ring: k ⟨ x , y ⟩ / ( y x − q x y ) {\displaystyle k\langle x,y\rangle /(yx-qxy)} More generally, the quantum polynomial ring is the
Noncommutative projective geometry
Noncommutative_projective_geometry
Algebraic structure in ring theory
spaces. A polynomial ring is a faithfully flat extension of its ring of coefficients. If p ∈ R [ x ] {\displaystyle p\in R[x]} is a monic polynomial, the inclusion
Flat_module
\delta ]} , also called a skew polynomial ring, is the noncommutative ring obtained by giving the ring of polynomials R [ x ] {\displaystyle R[x]} a new
Ore_extension
Type of algebra
defined by ring homomorphism f : R → A {\displaystyle f:R\to A} , such that every element of A {\displaystyle A} can be expressed as a polynomial in a finite
Finitely_generated_algebra
Algebraic study of differential equations
solutions, similarly as polynomial algebras are used for the study of algebraic varieties, which are solution sets of systems of polynomial equations. Weyl algebras
Differential_algebra
Formal power series with coefficients tending to 0
complete fields. Over a discrete topological ring, the ring of restricted power series coincides with a polynomial ring; thus, in this sense, the notion of "restricted
Restricted_power_series
Integer-valued polynomial Algebraic equation Factor theorem Polynomial remainder theorem See also Theory of equations below. Polynomial ring Greatest common
List_of_polynomial_topics
Polynomial with integer value for integer input
integer-valued polynomials was described fully by George Pólya (1915). Inside the polynomial ring Q [ t ] {\displaystyle \mathbb {Q} [t]} of polynomials with rational
Integer-valued_polynomial
Ring that is also a vector space or a module
the complex numbers are not in the center of the quaternions). Every polynomial ring R[x1, ..., xn] is a commutative R-algebra. In fact, this is the free
Associative_algebra
the Kostant polynomials, named after Bertram Kostant, provide an explicit basis of the ring of polynomials over the ring of polynomials invariant under
Kostant_polynomial
Computational problem used in cryptography
quotient polynomial ring R = Z [ x ] / ( x n − 1 ) {\displaystyle R=\mathbb {Z} [x]/(x^{n}-1)} are cyclic: consider the quotient polynomial ring R = Z [
Short integer solution problem
Short_integer_solution_problem
Type of algebraic structure
R_{i}=0} for i ≠ 0. This is called the trivial gradation on R. The polynomial ring R = k [ t 1 , … , t n ] {\displaystyle R=k[t_{1},\ldots ,t_{n}]} is
Graded_ring
xJ⊆I. [] R[x,y,...] is a polynomial ring over R. [[]] R[[x,y,...]] is a formal power series ring over R. {} R{x,y,...} is a ring of formal power series
Glossary of commutative algebra
Glossary_of_commutative_algebra
Algebraic structure in linear algebra
all polynomials p ( t ) {\displaystyle p(t)} forms an algebra known as the polynomial ring: using that the sum of two polynomials is a polynomial, they
Vector_space
Algebraic structure with addition, multiplication, and division
the residue field of R. The ideal generated by a single polynomial f in the polynomial ring R = E[X] (over a field E) is maximal if and only if f is
Field_(mathematics)
Abstract algebra concept
itself. For any field k, the field of fractions of the one-variable polynomial ring k [ t ] {\displaystyle k[t]} is the rational function field k ( t )
Field_of_fractions
Tool for solving polynomial equations
P(F(X))=0} where P {\displaystyle P} is a polynomial with coefficients in K [ X ] {\displaystyle K[X]} , the polynomial ring; that is, implicitly defined algebraic
Newton_polygon
Reduction of a ring by one of its ideals
quotient ring Z / n Z {\displaystyle \mathbb {Z} /n\mathbb {Z} } (which has n {\displaystyle n} elements). Now consider the ring of polynomials in the variable
Quotient_ring
Polynomial invariant under variable permutations
symmetric polynomial is a polynomial P(X1, X2, ..., Xn) in n variables, such that if any of the variables are interchanged, one obtains the same polynomial. Formally
Symmetric_polynomial
bracket ring is the subring of the ring of polynomials k[x11,...,xdn] generated by the d-by-d minors of a generic d-by-n matrix (xij). The bracket ring may
Bracket_ring
Generalization of algebraic variety
ideals in a polynomial ring) to the study of prime ideals in any commutative ring. For example, Krull defined the dimension of a commutative ring in terms
Scheme_(mathematics)
In mathematics, a Stanley–Reisner ring, or face ring, is a quotient of a polynomial algebra over a field by a square-free monomial ideal. Such ideals
Stanley–Reisner_ring
where the zi, j are new unknowns. Linear algebra is effective on the polynomial ring R [ x 1 , … , x n ] {\displaystyle R[x_{1},\ldots ,x_{n}]} if and only
Linear_equation_over_a_ring
Branch of mathematics
identified with the ring of polynomial functions in n variables over k. Therefore, the set of the regular functions on An is a ring, which is denoted k[An]
Algebraic_geometry
be a projective variety with the homogeneous coordinate ring S/I, where S is a polynomial ring. If H = { f = 0 } ⊂ P n {\displaystyle H=\{f=0\}\subset
Scheme-theoretic_intersection
1 {\displaystyle F_{1}} is a polynomial ring in one variable. For example, a central polynomial is an element of the ring F n {\displaystyle F_{n}} that
Generic_matrix_ring
Algorithm checking for prime numbers
{\displaystyle n} is prime if and only if the polynomial congruence relation holds within the polynomial ring ( Z / n Z ) [ X ] {\displaystyle (\mathbb {Z}
AKS_primality_test
Branch of mathematics
equation led to the Galois group of a polynomial. Gauss's 1801 study of Fermat's little theorem led to the ring of integers modulo n, the multiplicative
Abstract_algebra
Theorem about cohomology rings
Armand Borel (1953), says the cohomology ring of a classifying space or a classifying stack is a polynomial ring. Atiyah–Bott formula Behrend 2003, Theorem
Borel's_theorem
Open problem in ring theory (mathematics)
shown to be true for various classes of rings, such as polynomial identity rings and right Noetherian rings, but a general solution remains elusive.
Köthe_conjecture
Sufficient condition for polynomial irreducibility
mathematics, Eisenstein's criterion gives a sufficient condition for a polynomial with integer coefficients to be irreducible over the rational numbers
Eisenstein's_criterion
perfect rings are defined analogously. Artinian rings are perfect. polynomial 1. A polynomial ring over a commutative ring R is a commutative ring consisting
Glossary_of_ring_theory
Concept in algebraic geometry
(in fact zero-dimensional) is given by the following quotient of a polynomial ring with infinitely many generators. Q [ x 1 , x 2 , x 3 , … ] ( x 1 ,
Noetherian_scheme
Manifold or algebraic variety of dimension n in a space of dimension n+1
of n. This is the geometric interpretation of the fact that, in a polynomial ring over a field, the height of an ideal is 1 if and only if the ideal
Hypersurface
Commutative ring with no zero divisors other than zero
\supset \cdots } Rings of polynomials are integral domains if the coefficients come from an integral domain. For instance, the ring Z [ x ] {\displaystyle
Integral_domain
Algorithms for polynomial evaluation
3)=2\cdot 2\cdot 3+2^{3}+4=24.} See also Polynomial ring § Polynomial evaluation For evaluating the univariate polynomial a n x n + a n − 1 x n − 1 + ⋯ + a 0
Polynomial_evaluation
Well-behaved sequence in a commutative ring
ideal (p), and in fact the local ring Z(p) has depth 1. For any field k, the elements x1, ..., xn in the polynomial ring A = k[x1, ..., xn] form a regular
Regular_sequence
Infinite sum that is considered independently from any notion of convergence
R} form a ring, commonly denoted by R [ [ x ] ] . {\displaystyle R[[x]].} (It can be seen as the (x)-adic completion of the polynomial ring R [ x ] ,
Formal_power_series
over finite fields, in particular multiplication of polynomials from GF(2)[X], the polynomial ring over GF(2). The operation is also known as an XOR multiplication
Carry-less_product
Mathematical element
an element b of a commutative ring B is said to be integral over a subring A of B if b is a root of some monic polynomial over A. If A, B are fields, then
Integral_element
Submodule of a mathematical ring
beyond number rings to the setting of polynomial rings and other commutative rings by David Hilbert and especially Emmy Noether. Given a ring R {\displaystyle
Ideal_(ring_theory)
Would relate vector bundles over a regular Noetherian ring and over a polynomial ring
conjecture relates vector bundles over a regular Noetherian ring A and over the polynomial ring A [ t 1 , … , t n ] {\displaystyle A[t_{1},\dots ,t_{n}]}
Bass–Quillen_conjecture
POLYNOMIAL RING
POLYNOMIAL RING
Surname or Lastname
English
English : variant of Hurst.Jewish (Ashkenazic) : ornamental name or nickname from Polish herszt ‘ringleader’, ‘chieftain’.
Boy/Male
Tamil
Sitadevi | ஸீதாதேவீ
Mudrapradayaka deliverer of the ring of Sita
Sitadevi | ஸீதாதேவீ
Surname or Lastname
English, German, and Dutch
English, German, and Dutch : metonymic occupational name for a maker of rings (from Middle English ring, Middle High German rinc, Middle Dutch ring), either to be worn as jewelry or as component parts of chain-mail, harnesses, and other objects. In part it may also have arisen as a nickname for a wearer of a ring.Scandinavian : from ring ‘ring’, probably an ornamental name but possibly applied in the same sense as 3 or 1.German : topographic name from Middle High German, Middle Low German rink, rinc ‘circle’.Irish (eastern County Cork) : reduced Anglicized form of Gaelic Ó Rinn (see Reen).
Surname or Lastname
English and German
English and German : variant of Ring 1.Perhaps a Rhenish short form of the Latin personal name Quirinus.
Girl/Female
Tamil
Mudrika | மூதà¯à®°à®¿à®•à®¾
Ring
Mudrika | மூதà¯à®°à®¿à®•à®¾
Boy/Male
English
Ring.
Surname or Lastname
English
English : patronymic from Dear 1.German : probably a variant of Döring (see Doering).
Girl/Female
Muslim
A ring
Surname or Lastname
English
English : patronymic from Dear 1.German (Döring) : see Doering.
Surname or Lastname
English
English : from the Old English personal name Hringwulf.German : from a short form of a Germanic personal name based on hring ‘ring’.German : metonymic occupational name for a ring maker (see Ringler).German : altered spelling of Ringel, an Old Prussian personal name.
Surname or Lastname
English
English : variant of Kestel.German : from Middle High German kezzel ‘kettle’, ‘cauldron’, hence a metonymic occupational name for a maker of copper cooking vessels, or alternatively a topographic and habitational name, from the same word in the sense ‘(ring-shaped) hollow’.Dutch and Belgian : habitational name from any of the places so named in the Belgian provinces of Antwerp and Limburg or the Dutch province of North Brabant.
Surname or Lastname
English
English : habitational name from places in Oxfordshire and West Sussex named Goring, from Old English GÄringas ‘people of GÄra’, a short form of the various compound names with the first element gÄr ‘spear’.German (Göring) : see Goering.
Surname or Lastname
English (of Norman origin)
English (of Norman origin) : from the Old French personal name Reinger, Rainger, composed of the Germanic elements ragin ‘advice’, ‘counsel’ + gÄr, gÄ“r ‘spear’, ‘lance’.English : occupational name for a maker of rings (see Ring 1) or for a bell ringer, from Middle English ring(en) ‘to ring’, Old English hringan.German : occupational name for a turner, someone who made objects by rotating them on a lathe or wheel.
Surname or Lastname
English, German, and Jewish (Ashkenazic)
English, German, and Jewish (Ashkenazic) : from the Middle English, German, or Yiddish elements gold + ring. As an English or German surname it is most probably a nickname for someone who wore a gold ring. As a Jewish surname it is generally an ornamental name.Scottish : habitational name from Goldring in the bailiary of Kylestewart.The name is found in England as early as 1230, when Thomas Goldring is recorded as holding property in Essex and Hertfordshire. The name was quite common in London, Sussex, and Hampshire from early times, and descendants of these bearers are now also well established in Canada. The first known bearer in Scotland is Thomas of Goldringe, who held land in Prestwick in 1511.
Boy/Male
Tamil
Ramachudamaniprada | ரமசஂதாநீபà¯à®°à®¤à®¾
Deliverer of ramas ring
Ramachudamaniprada | ரமசஂதாநீபà¯à®°à®¤à®¾
Surname or Lastname
English
English : of uncertain origin. It is first attested in Norwich in 1259 as Ringerose, and later forms show no significant variantion. Unless it had already been drastically altered by folk etymology at that early date, it is probably from Middle English ring ‘ring’ + rose ‘rose’, but if so the original meaning is far from clear.
Boy/Male
Australian, British, English, French, German, Japanese
Ring; Apple; Peace be with You
Surname or Lastname
English
English : habitational name from places in Cumbria, Lincolnshire, and Northamptonshire. The first gets its name from Old English HaferingtÅ«n ‘settlement (Old English tÅ«n) associated with someone called Hæfer’, a byname meaning ‘he-goat’. The second probably meant ‘settlement (Old English tÅ«n) of someone called Hæring’. Alternatively, the first element may have been Old English hæring ‘stony place’ or hÄring ‘gray wood’. The last, recorded in Domesday Book as Arintone and in 1184 as Hederingeton, is most probably named with an unattested Old English personal name, Heathuhere.Irish (County Kerry and the West) : adopted as an Anglicized form of Gaelic Ó hArrachtáin ‘descendant of Arrachtán’, a personal name from a diminutive of arrachtach ‘mighty’, ‘powerful’.Irish (County Kerry) : adopted as an Anglicized form of Gaelic Ó hIongardail, later Ó hUrdáil, ‘descendant of Iongardal’.Irish : reduced Anglicized form of Gaelic Ó hOireachtaigh ‘descendant of Oireachtach’, a byname meaning ‘member of the assembly’ or ‘frequenting assemblies’.
Girl/Female
Tamil
Anumika | அநà¯à®‚மிகாÂ
Ring finger
Anumika | அநà¯à®‚மிகாÂ
Girl/Female
Tamil
Anamika | அநாமிகா
Ring finger, Virtuous, Free of the limitations imposed by a name
POLYNOMIAL RING
POLYNOMIAL RING
Surname or Lastname
English
English : variant of Dunkley.
Girl/Female
Gujarati, Indian
Good Character
Surname or Lastname
English
English : variant spelling of Bradbury.
Boy/Male
American, Australian, British, English, Greek
Tame; Saint Damian was the Patron Saint of Hairdressers
Female
Spanish
Spanish feminine form of Latin Crescentius, CRESCENCIA means "to spring up, grow, thrive."
Surname or Lastname
English
English : occupational name for a wool-packer, from an agent derivative of Middle English pack(en) ‘to pack’.German and Jewish (Ashkenazic) : from an agent derivative of Middle Low German pak, German Pack ‘package’, hence an occupational name for a wholesale trader, especially in the wool trade, one who sold goods in large packages rather than broken down into smaller quantities, or alternatively one who rode or drove pack animals to transport goods.
Surname or Lastname
English
English : nickname for an irascible person, from Old English wēd ‘fury’, ‘rage’.Americanized form of Dutch Weeda.
Boy/Male
Indian
The Fourth Veda; Name of Lord Ganesha
Boy/Male
Australian, Danish, Dutch, Greek, Swedish
People of Victory; Victory of the People
Boy/Male
Arabic
Free; Of Noble Birth
POLYNOMIAL RING
POLYNOMIAL RING
POLYNOMIAL RING
POLYNOMIAL RING
POLYNOMIAL RING
n. & a.
Same as Polynomial.
pl.
of Ringman
a.
Consisting of two or more words; having names consisting of two or more words; as, a polynomial name; polynomial nomenclature.
a.
Having a well defined ring of color around the neck.
n.
Any one of several species of small plovers of the genus Aegialitis, having a ring around the neck. The ring is black in summer, but becomes brown or gray in winter. The semipalmated plover (Ae. semipalmata) and the piping plover (Ae. meloda) are common North American species. Called also ring plover, and ring-necked plover.
n.
A polynomial name or term.
a.
Ring-streaked.
n.
An expression composed of two or more terms, connected by the signs plus or minus; as, a2 - 2ab + b2.
n.
A light sail set abaft and beyong the leech of a boom-and-gaff sail; -- called also ringsail.
n.
A game in which the object is to toss a ring so that it will catch upon an upright stick.
n.
The ring finger.
n.
A polynomial of four terms connected by the signs plus or minus.
a.
Containing many names or terms; multinominal; as, the polynomial theorem.
n.
The ring-necked duck.
n.
One in charge of the performances (as of horses) within the ring in a circus.
a.
Possessing the same number of factors of a given kind; as, a homogeneous polynomial.
a.
Having circular streaks or lines on the body; as, ring-streaked goats.
n.
A small ring; a small circle; specifically, a fairy ring.
n.
See Ringtail, 2.
n.
A contagious affection of the skin due to the presence of a vegetable parasite, and forming ring-shaped discolored patches covered with vesicles or powdery scales. It occurs either on the body, the face, or the scalp. Different varieties are distinguished as Tinea circinata, Tinea tonsurans, etc., but all are caused by the same parasite (a species of Trichophyton).