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Set with operations obeying given axioms
In mathematics, an algebraic structure or algebraic system consists of a nonempty set A (called the underlying set, carrier set or domain), a collection
Algebraic_structure
abstract algebra, a structurable algebra is a certain kind of unital involutive non-associative algebra over a field. For example, all Jordan algebras are
Structurable_algebra
Ring that is also a vector space or a module
a ring homomorphism from K into the center of A. This is thus an algebraic structure with an addition, a multiplication, and a scalar multiplication (the
Associative_algebra
Overview of and topical guide to algebraic structures
algebraic structures are studied. Abstract algebra is primarily the study of specific algebraic structures and their properties. Algebraic structures
Outline of algebraic structures
Outline_of_algebraic_structures
Algebraic structure modeling logical operations
In mathematics, a Boolean algebra or Boolean lattice is a complemented distributive lattice. This type of algebraic structure captures essential properties
Boolean_algebra_(structure)
Branch of mathematics
Algebra is a branch of mathematics that deals with abstract systems, known as algebraic structures, and the manipulation of expressions within those systems
Algebra
Albert algebra gives a form of the E7 Lie algebra. The split Albert algebra is used in a construction of a 56-dimensional structurable algebra whose automorphism
Albert_algebra
Algebra based on a vector space with a quadratic form
Clifford algebra is an algebra generated by a vector space with a quadratic form, and is a unital associative algebra with the additional structure of a distinguished
Clifford_algebra
Vector space equipped with a bilinear product
algebra over a field (often simply called an algebra) is a vector space equipped with a bilinear product. Thus, an algebra is an algebraic structure consisting
Algebra_over_a_field
Branch of mathematics
In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures, which are sets with specific operations
Abstract_algebra
Branch of mathematics
Linear algebra is the branch of mathematics concerning linear equations such as a 1 x 1 + ⋯ + a n x n = b , {\displaystyle a_{1}x_{1}+\cdots +a_{n}x_{n}=b
Linear_algebra
Branch of functional analysis
In functional analysis, a branch of mathematics, an operator algebra is an algebra of continuous linear operators on a topological vector space, with
Operator_algebra
Algebraic structure used in analysis
In mathematics, a Lie algebra (pronounced /liː/ LEE) is a vector space g {\displaystyle {\mathfrak {g}}} together with an operation called the Lie bracket
Lie_algebra
algebra Structurable algebra Supercommutative algebra Symmetric algebra Tensor algebra Universal enveloping algebra Vertex operator algebra von Neumann
List_of_algebras
Basic concepts of algebra
{b^{2}-4ac}}}{2a}}}}}} Elementary algebra, also known as high school algebra or college algebra, encompasses the basic concepts of algebra. It is often contrasted
Elementary_algebra
Mathematical structure in abstract algebra
more specifically in abstract algebra, a *-algebra (or involutive algebra; read as "star-algebra") is a mathematical structure consisting of two involutive
*-algebra
Algebraic structure with a binary operation
In abstract algebra, a magma, binar, or, rarely, groupoid is a basic kind of algebraic structure. Specifically, a magma consists of a set equipped with
Magma_(algebra)
Not-necessarily-associative commutative algebra satisfying (xy)(xx) = x(y(xx))
In abstract algebra, a Jordan algebra is a nonassociative algebra (with unit) over a field whose multiplication satisfies the following axioms: x y =
Jordan_algebra
Algebraic manipulation of "true" and "false"
mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables
Boolean_algebra
Theory of algebraic structures in general
algebra (sometimes called general algebra) is the field of mathematics that studies algebraic structures in general, not specific types of algebraic structures
Universal_algebra
248-dimensional exceptional simple Lie group
of Brown's 56-dimensional structurable algebra. Allison's 5-graded Lie algebra construction based on this structurable algebra recovers the original e 8
E8_(mathematics)
Associative algebra together with a Lie bracket that satisfies Leibniz's law
algebras appear naturally in Hamiltonian mechanics, and are also central in the study of quantum groups. Manifolds with a Poisson algebra structure are
Poisson_algebra
Algebraic structure of set algebra
a σ-algebra ("sigma algebra") is part of the formalism for defining sets that can be measured. In calculus and analysis, for example, σ-algebras are used
Σ-algebra
Particular kind of algebraic structure
mathematics, especially functional analysis, a Banach algebra, named after Stefan Banach, is an associative algebra A {\displaystyle A} over the real or complex
Banach_algebra
Elements taken to zero by a homomorphism
the underlying algebraic structure in the domain to its image. When the algebraic structures involved have an underlying group structure, the kernel is
Kernel_(algebra)
Study of discrete mathematical structures
function fields. Algebraic structures occur as both discrete examples and continuous examples. Discrete algebras include: Boolean algebra used in logic gates
Discrete_mathematics
Algebraic structure used in logic
In mathematics, a Heyting algebra (also known as pseudo-Boolean algebra) is a bounded lattice (with join and meet operations written ∨ and ∧ and with
Heyting_algebra
Algebraic structure designed for geometry
geometric algebra (also known as a Clifford algebra) is an algebra that can represent and manipulate geometrical objects such as vectors. Geometric algebra is
Geometric_algebra
Construction in algebra
In mathematics, a Hopf algebra, named after Heinz Hopf, is a structure that is simultaneously a (unital associative) algebra and a (counital coassociative)
Hopf_algebra
Topological complex vector space
mathematics, specifically in functional analysis, a C∗-algebra (pronounced "C-star") is a Banach algebra together with an involution satisfying the properties
C*-algebra
Additional mathematical object
partial list of possible structures is measures, algebraic structures (groups, fields, etc.), topologies, metric structures (geometries), orders, graphs
Mathematical_structure
Class of algebraic structures
In universal algebra, a variety of algebras or equational class is the class of all algebraic structures of a given signature satisfying a given set of
Variety_(universal_algebra)
Application of mathematical methods to other fields
as a collection of mathematical methods such as real analysis, linear algebra, mathematical modelling, optimisation, combinatorics, probability and statistics
Applied_mathematics
Algebraic structure with addition, multiplication, and division
rational numbers do. A field is thus a fundamental algebraic structure that is widely used in algebra, number theory, and many other areas of mathematics
Field_(mathematics)
Algebraic structure with only one element
In algebra, the zero object of a given algebraic structure is, in the sense explained below, the simplest object of such structure. As a set it is a singleton
Zero_object_(algebra)
Algebra over a field where binary multiplication is not necessarily associative
operation is not assumed to be associative. That is, an algebraic structure A is a non-associative algebra over a field K if it is a vector space over K and
Non-associative_algebra
Mapping of mathematical formulas to a particular meaning
Universal algebra studies structures that generalize the algebraic structures such as groups, rings, fields and vector spaces. The term universal algebra is
Structure (mathematical logic)
Structure_(mathematical_logic)
Algebraic structure in homological algebra
homological algebra, algebraic topology, and algebraic geometry – a differential graded algebra (or DGA, or DG algebra) is an algebraic structure often used
Differential_graded_algebra
Algebraic structure with addition and multiplication
In mathematics, a ring is an algebraic structure consisting of a set with two binary operations typically called addition and multiplication and denoted
Ring_(mathematics)
supersymmetry algebra (or SUSY algebra) is a mathematical formalism for describing the relation between bosons and fermions. The supersymmetry algebra contains
Supersymmetry_algebra
Area of mathematics
algorithm design, computational complexity, numerical methods and computer algebra. Computational mathematics refers also to the use of computers for mathematics
Computational_mathematics
computer algebra system (CAS) is a software product designed for manipulation of mathematical formulae. The principal objective of a computer algebra system
List of open-source software for mathematics
List_of_open-source_software_for_mathematics
Calculus of vector-valued functions
generalize to higher dimensions, but the alternative approach of geometric algebra, which uses the exterior product, does (see § Generalizations below for
Vector_calculus
Universal construction in multilinear algebra
algebra, Clifford algebras, the Weyl algebra and universal enveloping algebras. The tensor algebra also has two coalgebra structures; one simple one, which
Tensor_algebra
Result of partitioning the elements of an algebraic structure using a congruence relation
a quotient algebra is the result of partitioning the elements of an algebraic structure using a congruence relation. Quotient algebras are also called
Quotient_(universal_algebra)
Algebraic structure
algebra, an interior algebra is a certain type of algebraic structure that encodes the idea of the topological interior of a set. Interior algebras are
Interior_algebra
Study of abstract machines and automata
nondeterministic finite automata. In the 1960s, a body of algebraic results known as "structure theory" or "algebraic decomposition theory" emerged, which dealt with
Automata_theory
Algebraic variety with a group structure
mathematics, an algebraic group is an algebraic variety endowed with a group structure that is compatible with its structure as an algebraic variety. Thus
Algebraic_group
Algebraic structure
In mathematics, a J-structure is an algebraic structure over a field related to a Jordan algebra. The concept was introduced by Springer (1973) to develop
J-structure
Algebra associated to any vector space
In mathematics, the exterior algebra or Grassmann algebra of a vector space V {\displaystyle V} is an associative algebra that contains V , {\displaystyle
Exterior_algebra
Branch of mathematics concerning probability
any set Ω {\displaystyle \Omega \,} (also called sample space) and a σ-algebra F {\displaystyle {\mathcal {F}}\,} on it, a measure P {\displaystyle \mathbb
Probability_theory
Sequence of operations for a task
beyond specific numerical solutions to introduce general procedures for algebraic reduction and balancing. This transformed mathematics into a 'mechanical'
Algorithm
Set whose pairs have minima and maxima
A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra. It consists of a partially ordered
Lattice_(order)
Magma obeying the Latin square property
In mathematics, especially in abstract algebra, a quasigroup is an algebraic structure that resembles a group in the sense that "division" is always possible
Quasigroup
Algebraic construct of interest in theoretical physics
noncommutative algebras with additional structure. These include Drinfeld–Jimbo type quantum groups (which are quasitriangular Hopf algebras), compact matrix
Quantum_group
Equivalence relation in algebra
In abstract algebra, a congruence relation (or simply congruence) is an equivalence relation on an algebraic structure (such as a group, ring, or vector
Congruence_relation
Coefficients of an algebra over a field
In mathematics, the structure constants or structure coefficients of an algebra over a field are the coefficients of the basis expansion (into linear
Structure_constants
Study of the properties of codes and their fitness
needed] The term algebraic coding theory denotes the sub-field of coding theory where the properties of codes are expressed in algebraic terms and then
Coding_theory
In algebraic geometry, a level structure on a space X is an extra structure attached to X that shrinks or eliminates the automorphism group of X, by demanding
Level structure (algebraic geometry)
Level_structure_(algebraic_geometry)
In mathematics, BCI and BCK algebras are algebraic structures in universal algebra, which were introduced by Y. Imai, K. Iséki and S. Tanaka in 1966, that
BCK_algebra
Computer system for solving algebra problems
computer algebra system designed to solve problems in algebra, number theory, geometry and combinatorics. It is named after the algebraic structure magma
Magma (computer algebra system)
Magma_(computer_algebra_system)
Branch of algebra that studies commutative rings
Commutative algebra, first known as ideal theory, is the branch of algebra that studies commutative rings, their ideals, and modules over such rings. Both
Commutative_algebra
algebra is an extension of vector algebra, providing additional algebraic structures on vector spaces, with geometric interpretations. Vector algebra
Comparison of vector algebra and geometric algebra
Comparison_of_vector_algebra_and_geometric_algebra
Field of mathematics
Numerical linear algebra, sometimes called applied linear algebra, is the study of how matrix operations can be used to create computer algorithms which
Numerical_linear_algebra
Algebraic structure providing a semantics of Łukasiewicz logic
In abstract algebra, a branch of pure mathematics, an MV-algebra is an algebraic structure with a binary operation ⊕ {\displaystyle \oplus } , a unary
MV-algebra
Unix-like systems. KCalc, Linux based scientific calculator Maxima: a computer algebra system which bignum integers are directly inherited from its implementation
List of arbitrary-precision arithmetic software
List_of_arbitrary-precision_arithmetic_software
Theory of subatomic structure
called algebraic varieties which are defined by the vanishing of polynomials. For example, the Clebsch cubic illustrated on the right is an algebraic variety
String_theory
Speech coding algorithm
coding (LPC) vocoders (e.g., FS-1015). Along with its variants, such as algebraic CELP, relaxed CELP, low-delay CELP and vector sum excited linear prediction
Code-excited linear prediction
Code-excited_linear_prediction
Set of objects whose state must satisfy limits
algebra. It turned out that questions about the complexity of CSPs translate into important universal-algebraic questions about underlying algebras.
Constraint satisfaction problem
Constraint_satisfaction_problem
Branch of mathematics that studies algebraic structures
algebra in Wiktionary, the free dictionary. In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures
List of abstract algebra topics
List_of_abstract_algebra_topics
Software used in mathematical applications
mathematical suites are computer algebra systems that use symbolic mathematics. They are designed to solve classical algebra equations and problems in human
Mathematical_software
Setting of relativistic physics in geometric algebra
spacetime algebra (STA) is the application of Clifford algebra Cl1,3(R), or equivalently the geometric algebra G(M4) of physics. Spacetime algebra provides
Spacetime_algebra
Group that is also a differentiable manifold with group operations that are smooth
circle. Its Lie algebra is (more or less) the Witt algebra, whose central extension the Virasoro algebra (see Virasoro algebra from Witt algebra for a derivation
Lie_group
Concept in mathematics
enveloping algebra of a Lie algebra is the unital associative algebra whose representations correspond precisely to the representations of that Lie algebra. Universal
Universal_enveloping_algebra
Algebra used in 2D conformal field theories and string theory
In mathematics, a vertex operator algebra (VOA) is an algebraic structure that plays an important role in two-dimensional conformal field theory and string
Vertex_operator_algebra
Freely generated algebraic structure over a given signature
In universal algebra and mathematical logic, a term algebra is a freely generated algebraic structure over a given signature. For example, in a signature
Term_algebra
Software for a class of mathematical problems
problems Systems of ordinary differential equations Systems of differential algebraic equations Boolean satisfiability problems, including SAT solvers Quantified
Solver
Left adjoint to a forgetful functor to sets
concepts of abstract algebra. Informally, a free object over a set A can be thought of as being a "generic" algebraic structure over A: the only equations
Free_object
Group of mathematical theorems
modules, Lie algebras, and other algebraic structures. In universal algebra, the isomorphism theorems can be generalized to the context of algebras and congruences
Isomorphism_theorems
Mathematical set with some added structure
should be considered as a geometric "space", or an algebraic "structure". A general definition of "structure", proposed by Bourbaki, embraces all common types
Space_(mathematics)
postulate. Abstract algebra The part of algebra devoted to the study of algebraic structures in themselves. Occasionally named modern algebra in course titles
Glossary of areas of mathematics
Glossary_of_areas_of_mathematics
Branch of mathematics
Homological algebra is the branch of mathematics that studies homology in a general algebraic setting. It is a relatively young discipline, whose origins
Homological_algebra
Branch of mathematics
aspects of the eigenvalue decomposition from linear algebra to infinite dimensions. As in linear algebra, it is often possible to understand an operator more
Mathematical_analysis
Getting better now but I'm still waiting for the time
special train algebras, gametic algebras, Bernstein algebras, copular algebras, zygotic algebras, and baric algebras (also called weighted algebra). The study
Genetic_algebra
Algebraic structure used in theoretical physics
superalgebra is a Z 2 {\displaystyle \mathbb {Z} _{2}} -graded algebra. That is, it is an algebra over a commutative ring or field with a decomposition into
Superalgebra
Finite extension of the rationals
theory. This study reveals hidden structures behind the rational numbers, by using algebraic methods. The notion of algebraic number field relies on the concept
Algebraic_number_field
Study of abstract algebraic structures
In abstract algebra, a representation of an associative algebra is a module for that algebra. Here an associative algebra is a (not necessarily unital)
Algebra_representation
Physical theory with fields invariant under the action of local "gauge" Lie groups
the gauge group of the theory. Associated with any Lie group is the Lie algebra of group generators. For each group generator there necessarily arises
Gauge_theory
Branch of mathematics that studies the properties of groups
In abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known
Group_theory
Algebraic ring without a multiplicative identity
In abstract algebra, a rng (pronounced "rung" /rʌŋ/) or non-unital ring or pseudo-ring is an algebraic structure satisfying the same properties as a ring
Rng_(algebra)
Branch of mathematics
Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants
Algebraic_topology
Generalization of vector spaces from fields to rings
central notions of commutative algebra and homological algebra, and are used widely in algebraic geometry and algebraic topology. In a vector space, the
Module_(mathematics)
Branch of mathematics
Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems
Algebraic_geometry
Boolean algebra with a derivative operator capturing change or boundary behavior
abstract algebra, a derivative algebra is an algebraic structure of the signature <A, ·, +, ', 0, 1, D> where <A, ·, +, ', 0, 1> is a Boolean algebra and D
Derivative algebra (abstract algebra)
Derivative_algebra_(abstract_algebra)
Study of categorified structures
higher-dimensional algebra is the study of categorified structures. It has applications in nonabelian algebraic topology, and generalizes abstract algebra. A first
Higher-dimensional_algebra
Branch of applied mathematics
some parts of the mathematical fields of linear algebra, the spectral theory of operators, operator algebras and, more broadly, functional analysis. Nonrelativistic
Mathematical_physics
1960 article by Eugene Wigner
beauty”, nevertheless often find applications in physics. The mathematical structure of theoretical physics often points the way to further advances in that
The Unreasonable Effectiveness of Mathematics in the Natural Sciences
The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences
Open convex self-dual cones
type. All the algebraic and geometric structures associated with the symmetric space can be expressed naturally in terms of the Jordan algebra. The other
Symmetric_cone
Formulation of classical mechanics using momenta
symplectic structure induces a Poisson bracket. The Poisson bracket gives the space of functions on the manifold the structure of a Lie algebra. If F and
Hamiltonian_mechanics
Function type in category theory
specifically in category theory, F-algebras generalize the notion of algebraic structure. Rewriting the algebraic laws in terms of morphisms eliminates
F-algebra
STRUCTURABLE ALGEBRA
STRUCTURABLE ALGEBRA
Surname or Lastname
English
English : occupational name for a wattler, Middle English watelere, i.e. someone who made the panels of interwoven twigs that were used to fill the spaces between the structural timbers of a timber frame building. See also Dauber.
STRUCTURABLE ALGEBRA
STRUCTURABLE ALGEBRA
Girl/Female
Norse
Heroic.
Female
German
 Feminine form of German Ernust, ERNA means "battle (to the death), serious business." Compare with another form of Erna.
Boy/Male
Hindu, Indian, Tamil
Devotee of Lord Kali
Girl/Female
Muslim
Flower
Boy/Male
Arabic, Muslim
One with Strong Imaan; Also a Sahabi; One of the Early Muslims
Surname or Lastname
English
English : unexplained.
Girl/Female
Arabic, Muslim, Pashtun
Truthful
Girl/Female
American, Australian, British, English
Juniper Tree; Phonetic Variant of Genevieve
Boy/Male
Muslim
To take revenge
Boy/Male
Irish
Hunch backed.
STRUCTURABLE ALGEBRA
STRUCTURABLE ALGEBRA
STRUCTURABLE ALGEBRA
STRUCTURABLE ALGEBRA
STRUCTURABLE ALGEBRA
a.
Pertaining to an edifice; structural.
n.
The syntactical or structural form peculiar to any language; the genius or cast of a language.
n.
An expression conforming or appropriate to the peculiar structural form of a language; in extend use, an expression sanctioned by usage, having a sense peculiar to itself and not agreeing with the logical sense of its structural form; also, the phrase forms peculiar to a particular author.
a.
Pertaining to homology; having a structural affinity proceeding from, or base upon, that kind of relation termed homology.
n.
A theoretical aggregation of molecules constituting a structural particle of protoplasm, capable of increase or diminution without change in chemical nature.
v. t.
To determine the homologies or structural relations of.
a.
Derived from epithelial cells and destined to become a part of the muscular system; -- applied to structural elements in certain embryonic forms.
a.
Of or pertaining to structure; affecting structure; as, a structural error.
a.
Comprising structural characters which are separated in more specialized forms; synthetic; as, a generalized type.
n.
Having the color spots, or structural parts, arranged spirally.
n.
Neuralgia of the kidneys; a disease characterized by pain in the region of the kidneys without any structural lesion of the latter.
a.
Fleshy; -- applied to the minute structural elements, called sarcous elements, or sarcous disks, of which striated muscular fiber is composed.
n.
The assumption of several structural forms without a corresponding difference in function; -- said of sponges, etc.
n.
A band; a structural line; -- applied to several bands and lines of nervous matter in the brain.
n.
A number of species or genera having certain structural characteristics in common; as, a tribe of plants; a tribe of animals.
n.
The classification of living organisms according to their structural character; taxonomy.
n.
An affection characterized by pain in or about a joint, not dependent upon structural disease.
a.
A typical, structural unit; a type.
a.
Not capable of self-fertilization; -- said of hermaphrodite flowers in which some structural obstacle forbids autogamy.
a.
Of or pertaining to organit structure; as, a structural element or cell; the structural peculiarities of an animal or a plant.