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See searches and references containing MODULE MATHEMATICS!MODULE MATHEMATICS
Generalization of vector spaces from fields to rings
In mathematics, a module is a generalization of the notion of vector space in which the field of scalars is replaced by a (not necessarily commutative)
Module_(mathematics)
Direct summand of a free module (mathematics)
In mathematics, particularly in algebra, the class of projective modules enlarges the class of free modules (that is, modules with basis vectors) over
Projective_module
In mathematics, a module that has a basis
mathematics, a free module is a module that has a basis, that is, a generating set that is linearly independent. Every vector space is a free module,
Free_module
Topics referred to by the same term
hardware Multi-chip module, a modern technique that combines several complex computer chips into a single larger unit Module (mathematics) over a ring, a
Module
In algebra, module with a finite generating set
In mathematics, a finitely generated module is a module that has a finite generating set. A finitely generated module over a ring R may also be called
Finitely_generated_module
Certain type of mathematics from secondary school onwards
from the core mathematics modules, the applied modules may start from first principles. The Edexcel exam board involves 2 Core Pure modules studied in school
Further_Mathematics
Mathematical object in abstract algebra
In mathematics, especially in the area of abstract algebra known as module theory, an injective module is a module Q that shares certain desirable properties
Injective_module
Algebraic structure in ring theory
algebra, flat modules include free modules, projective modules, and, over a principal ideal domain, torsion-free modules. Formally, a module M over a ring
Flat_module
Algebraic structure with addition and multiplication
ISBN 0-226-42454-5, MR 0345945 Lam, Tsit Yuen (1999). Lectures on modules and rings. Graduate Texts in Mathematics. Vol. 189. Springer. ISBN 0-387-98428-3. Lam, Tsit
Ring_(mathematics)
In mathematics, more specifically in ring theory, a cyclic module or monogenous module is a module over a ring that is generated by one element. The concept
Cyclic_module
Direct sum of irreducible modules
In mathematics, especially in the area of abstract algebra known as module theory, a semisimple module or completely reducible module is a type of module
Semisimple_module
Notion in abstract algebra
In mathematics, particularly in algebra, the injective hull (or injective envelope) of a module is both the smallest injective module containing it and
Injective_hull
Elements of a field, e.g. real numbers, in the context of linear algebra
In mathematics, more specifically in linear algebra, a scalar is an element of a field which is used to define a vector space through the operation of
Scalar_(mathematics)
Module over a sheaf of differential operators
In mathematics, a D-module is a module over a ring D of differential operators. The major interest of such D-modules is as an approach to the theory of
D-module
Types of mappings in mathematics
on Mathematics. New York: Dover Books. ISBN 978-1-61427-304-2. OCLC 912495626. Lang, Serge (2002), "III. Modules, §6. The dual space and dual module",
Functional_(mathematics)
Operation that pairs a left and a right R-module into an abelian group
In mathematics, the tensor product of modules is a construction that allows arguments about bilinear maps (e.g. multiplication) to be carried out in terms
Tensor_product_of_modules
In mathematics, the dual module of a left (respectively right) module M over a ring R is the set of left (respectively right) R-module homomorphisms from
Dual_module
Field of knowledge
and true mathematical assertions, but appear to be nonsense to people who do not have the required background. For example, "every free module is flat"
Mathematics
In the context of a module M over a ring R, the top of M is the largest semisimple quotient module of M if it exists. For finite-dimensional k-algebras
Top_(algebra)
In mathematics, a stably free module is a module which is close to being free. A module M over a ring R is stably free if there exists a free finitely
Stably_free_module
Concept in mathematics
In mathematics, a Drinfeld module (or elliptic module) is roughly a special kind of module over a ring of functions on a curve over a finite field, generalizing
Drinfeld_module
Form of written communication for math
the definitions of basis, module, and free module. H. B. Williams, an electrophysiologist, wrote in 1927: Now mathematics is both a body of truth and
Language_of_mathematics
Representation of symmetric groups
In mathematics, a Specht module is one of the representations of symmetric groups studied by Wilhelm Specht (1935). They are indexed by partitions, and
Specht_module
Ideal that maps to zero a subset of a module
In mathematics, the annihilator of a subset S of a module over a ring is the ideal formed by the elements of the ring that always give zero when multiplied
Annihilator_(ring_theory)
In mathematics, the Jacquet module is a module used in the study of automorphic representations. The Jacquet functor is the functor that sends a linear
Jacquet_module
Modular translation unit in C++
module must be declared using the word module to indicate that the translation unit is a module. A module, once compiled, is stored as a built module
Modules_(C++)
Mathematical terminology
In mathematics, a Galois module is a G-module, with G being the Galois group (named for Évariste Galois) of some extension of fields. The term Galois representation
Galois_representation
Topic in abstract algebra
Butler (1980, p. 103) In mathematics, specifically representation theory, tilting theory describes a way to relate the module categories of two algebras
Tilting_theory
Algebraic structure
In mathematics, given a group G {\displaystyle G} , a G-module is an abelian group M {\displaystyle M} on which G {\displaystyle G} acts compatibly with
G-module
Linear map over a ring
algebra, a module homomorphism is a function between modules that preserves the module structures. Explicitly, if M and N are left modules over a ring
Module_homomorphism
In mathematics, a topological module is a module over a topological ring such that scalar multiplication and addition are continuous. A module topology
Topological_module
Zero divisors in a module
In mathematics, specifically in ring theory, a torsion element is an element of a module that yields zero when multiplied by some non-zero-divisor of
Torsion_(algebra)
Type of module over a ring
In mathematics, specifically in ring theory, the simple modules over a ring R are the (left or right) modules over R that are non-zero and have no non-zero
Simple_module
A persistence module is a mathematical structure in persistent homology and topological data analysis that formally captures the persistence of topological
Persistence_module
Module theory is the branch of mathematics in which modules are studied. This is a glossary of some terms of the subject. See also: Glossary of linear
Glossary_of_module_theory
Algebraic structure with only one element
a module (over a ring R), the zero module. The term trivial module is also used, although it may be ambiguous, as a trivial G-module is a G-module with
Zero_object_(algebra)
American series of educational videos
Project Mathematics! (stylized as Project MATHEMATICS!), is a series of educational video modules and accompanying workbooks for teachers, developed at
Project_Mathematics!
In mathematics, in the theory of modules, the radical of a module is a component in the theory of structure and classification. It is a generalization
Radical_of_a_module
Construction of a ring of fractions
"denominators" to a given ring or module. That is, it introduces a new ring/module out of an existing ring/module R, so that it consists of fractions
Localization (commutative algebra)
Localization_(commutative_algebra)
Pure-injective modules in mathematics
In mathematics, algebraically compact modules, also called pure-injective modules, are modules that have a certain "nice" property which allows the solution
Algebraically_compact_module
Abstract algebra module
In abstract algebra, a Noetherian module is a module that satisfies the ascending chain condition on its submodules, where the submodules are partially
Noetherian_module
Branch of mathematics that studies algebraic structures
Inverse Galois problem Kummer theory Module (mathematics) Bimodule Annihilator (ring theory) Submodule Pure submodule Module homomorphism Essential submodule
List of abstract algebra topics
List_of_abstract_algebra_topics
Monster and modular connection
bridge between two mathematical areas. The conjectures made by Conway and Norton were proven by Richard Borcherds for the moonshine module in 1992 using the
Monstrous_moonshine
Term in mathematics
In mathematics, a characterization of an object is a set of conditions that, while possibly different from the definition of the object, is logically
Characterization (mathematics)
Characterization_(mathematics)
Statement in abstract algebra
In mathematics, in the field of abstract algebra, the structure theorem for finitely generated modules over a principal ideal domain is a generalization
Structure theorem for finitely generated modules over a principal ideal domain
Structure_theorem_for_finitely_generated_modules_over_a_principal_ideal_domain
Index of articles associated with the same name
of Modules. Springer-Verlag. ISBN 978-0-387-97845-1. Robinson, Derek J. S. (1996), A course in the theory of groups, Graduate Texts in Mathematics, vol
Socle_(mathematics)
Mathematical ring with well-behaved ideals
Frank W.; Fuller, Kent R. (1992), Rings and categories of modules, Graduate Texts in Mathematics, vol. 13 (2 ed.), New York: Springer-Verlag, pp. x+376,
Noetherian_ring
Overview of and topical guide to discrete mathematics
Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have
Outline of discrete mathematics
Outline_of_discrete_mathematics
Equivalence relation on rings
their modules, as modules can be viewed as representations of rings. Every ring R has a natural R-module structure on itself where the module action
Morita_equivalence
In mathematics, particularly commutative algebra, an invertible module is intuitively a module that has an inverse with respect to the tensor product
Invertible_module
In mathematics, especially in the area of abstract algebra, every module has an associated character module. Using the associated character module it
Character_module
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
In mathematics, particularly in the field of ring theory, a lattice is an algebraic structure which, informally, provides a general framework for taking
Lattice_(module)
Exact sequence used to describe the structure of an object
modules (or, more generally, of objects of an abelian category) that is used to define invariants characterizing the structure of a specific module or
Resolution_(algebra)
Array of numbers
ISBN 978-0-19-852211-9, MR 0969370 Lam, T. Y. (1999), Lectures on Modules and Rings, Graduate Texts in Mathematics, vol. 189, Springer-Verlag, New York, doi:10.1007/978-1-4612-0525-8
Matrix_(mathematics)
Algebraic structure
In mathematics, a Tate module of an abelian group, named for John Tate, is a module constructed from an abelian group A. Often, this construction is made
Tate_module
Le Corbusier's anthropometric scale of proportions
entrance ramp would be "visible essay on the mathematics of the human body". In this image of the Modulor in Berlin, there are several messages cast in
Modulor
Sheaf consisting of modules on a ringed space; generalizing vector bundles
In mathematics, a sheaf of O-modules or simply an O-module over a ringed space (X, O) is a sheaf of abelian groups F such that, for any open subset U
Sheaf_of_modules
Type of mathematical equation
linear relation, or simply relation, between elements of a vector space or a module is a linear equation that has these elements as a solution. More precisely
Linear_relation
quasi-isomorphic to a bounded complex of finite projective A-modules. A perfect module is a module that is perfect when it is viewed as a complex concentrated
Perfect_complex
Describes the objects of a given type, up to some equivalence
In mathematics, a classification theorem answers the classification problem: "What are the objects of a given type, up to some equivalence?". It gives
Classification_theorem
Prime ideal that is an annihilator of a prime submodule
Texts in Mathematics, vol. 150, Berlin, New York: Springer-Verlag, ISBN 978-0-387-94268-1, MR 1322960 Lam, Tsit Yuen (1999), Lectures on modules and rings
Associated_prime
ISBN 3-540-64239-0. Lam, Tsit Yuen (1999). Lectures on modules and rings. Graduate Texts in Mathematics No. 189. Berlin, New York: Springer-Verlag. p. 146
Torsionless_module
Tool to track locally defined data attached to the open sets of a topological space
Look up sheaf in Wiktionary, the free dictionary. In mathematics, a sheaf (pl.: sheaves) is a tool for systematically tracking data (such as sets, abelian
Sheaf_(mathematics)
In mathematics, dimension of a ring
Noetherian ring. More generally the Krull dimension can be defined for modules over possibly non-commutative rings as the deviation of the poset of submodules
Krull_dimension
Module over the non-commutative Dieudonné ring
In mathematics, a Dieudonné module introduced by Jean Dieudonné (1954, 1957b), is a module over the non-commutative Dieudonné ring, which is generated
Dieudonné_module
Type of commutative ring in mathematics
local ring is Cohen–Macaulay exactly when it is a finitely generated free module over a regular local subring. Cohen–Macaulay rings play a central role in
Cohen–Macaulay_ring
Objects in representation theory of Lie algebras
Verma modules, named after Daya-Nand Verma, are objects in the representation theory of Lie algebras, a branch of mathematics. Verma modules can be used
Verma_module
In abstract algebra, a module is called a uniform module if the intersection of any two nonzero submodules is nonzero. This is equivalent to saying that
Uniform_module
Algebraic construction
In algebra, given a module and a submodule, one can construct their quotient module. This construction, described below, is very similar to that of a
Quotient_module
Abelian group in which every element can, in some sense, be divided by positive integers
Academic Press. Lam, Tsit-Yuen (1999), Lectures on modules and rings, Graduate Texts in Mathematics No. 189, vol. 189, Berlin, New York: Springer-Verlag
Divisible_group
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation
Glossary of mathematical symbols
Glossary_of_mathematical_symbols
Educational qualification in the UK
consisted of six modules, four pure modules (C1, C2, C3, and C4) and two applied modules in Statistics, Mechanics and/or Decision Mathematics. The C1 through
Advanced_level_mathematics
Commutative algebra studies commutative rings, their ideals, and modules over such rings
multiplicity conjectures Homological conjectures Commutative ring Module (mathematics) Ring ideal, maximal ideal, prime ideal Ring homomorphism Ring monomorphism
List of commutative algebra topics
List_of_commutative_algebra_topics
Mathematician
especially the theory of automorphic forms, through the notions of elliptic module and the theory of the geometric Langlands correspondence. Drinfeld introduced
Vladimir_Drinfeld
On polynomial rings over fields
between the generators of an ideal, or, more generally, a module. As the relations form a module, one may consider the relations between the relations; the
Hilbert's_syzygy_theorem
In abstract algebra, a dualizing module, also called a canonical module, is a module over a commutative ring that is analogous to the canonical bundle
Dualizing_module
Type of algebraic structure
words, we require A to be a graded left module over R. Examples of graded algebras are common in mathematics: Polynomial rings. The homogeneous elements
Graded_ring
Topics referred to by the same term
Development (Brunei) Mod, a module for Apache HTTP Server Case modding of a computer Forum moderator, of an online forum Module file, a music file format
Mod
Practical mathematics used in business
(instead) include a module in "mathematics for economists", providing a bridge between the above "Business Mathematics" courses and mathematical economics and
Business_mathematics
Module over a ring
Tag 0AVQ. "Torsion-free_module", Encyclopedia of Mathematics, EMS Press, 2001 [1994] Matlis, Eben (1972), Torsion-free modules, The University of Chicago
Torsion-free_module
Emerging field of applied ethics
Ethics in mathematics is an emerging field of applied ethics, the inquiry into ethical aspects of the practice and applications of mathematics. It deals
Ethics_in_mathematics
Mathematical property
In mathematics, semi-simplicity is a widespread concept in disciplines such as linear algebra, abstract algebra, representation theory, category theory
Semi-simplicity
Operation in abstract algebra
combines several modules into a new, larger module. The direct sum of modules is the smallest module which contains the given modules as submodules with
Direct_sum_of_modules
In mathematics, a continuous module is a module M such that every submodule of M is essential in a direct summand and every submodule of M isomorphic to
Continuous_module
In mathematics, especially representation theory, the stable module category is a quotient of a module category in which projectives are "factored out
Stable_module_category
Invariant of rings and modules
invariant of rings and modules. Although depth can be defined more generally, the most common case considered is the case of modules over a commutative Noetherian
Depth_(ring_theory)
Japanese mathematician (born 1947)
the study of D-modules. He continued studying under Sato at Kyoto University after Sato moved to the Research Institute for Mathematical Sciences (RIMS)
Masaki_Kashiwara
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Construction in homological algebra
category of modules over R {\displaystyle R} . (One can take this to mean either left R {\displaystyle R} -modules or right R {\displaystyle R} -modules.) For
Ext_functor
Mathematical relation in abstract algrebra
R-module. Let M be a left S-module and N a left R-module. By restriction of scalars, M is also a left R-module. If S is projective as a right R-module,
Shapiro's_lemma
}I^{n}/I^{n+1}} . Similarly, if M is a left R-module, then the associated graded module is the graded module over gr I R {\displaystyle \operatorname {gr}
Associated_graded_ring
Objects between rings and their fields of fractions
In mathematics, almost modules and almost rings are certain objects interpolating between rings and their fields of fractions. They were introduced by
Almost_ring
Group of mathematical theorems
subobjects. Versions of the theorems exist for groups, rings, vector spaces, modules, Lie algebras, and other algebraic structures. In universal algebra, the
Isomorphism_theorems
Study of discrete mathematical structures
(2009). Resources for Teaching Discrete Mathematics: Classroom Projects, History Modules, and Articles. Mathematical Association of America. ISBN 978-0-88385-184-5
Discrete_mathematics
Scalar-valued bilinear function
Weintraub, Steven H. (1992), Algebra: An Approach via Module Theory, Graduate Texts in Mathematics, vol. 136, Springer-Verlag, ISBN 3-540-97839-9, Zbl 0768
Bilinear_form
In mathematics a Yetter–Drinfeld category is a special type of braided monoidal category. It consists of modules over a Hopf algebra which satisfy some
Yetter–Drinfeld_category
Module generated by a countable subset
In mathematics, a module over a (not necessarily commutative) ring is countably generated if it is generated as a module by a countable subset. The importance
Countably_generated_module
Analysis of datasets using techniques from topology
persistence modules". arXiv:1207.3674 [math.AT]. Webb, Cary (1985-01-01). "Decomposition of graded modules". Proceedings of the American Mathematical Society
Topological_data_analysis
Concept in category theory
In mathematics, more specifically in the area of category theory, a forgetful functor (also known as a stripping functor) "forgets" or drops some or all
Forgetful_functor
MODULE MATHEMATICS
MODULE MATHEMATICS
Boy/Male
Hindu
Name of Lord Shiva
Female
French
Feminine form of French Odilon, ODILE means "wealthy."
Surname or Lastname
English
English : of uncertain origin; perhaps derived from the vocabulary word soul as a term of affection.French (Soulé) : variant of Soulier 1.George Soule (1600–80), one of the passengers on the Mayflower in 1620, was one of the founders of Duxbury, MA, where he became comparatively wealthy. He left eight children.
Surname or Lastname
German (Mäule)
German (Mäule) : variant of Maul 1.English : variant of Maul 2.
Surname or Lastname
French
French : from a reduced form of the Germanic personal name Hildo (see Hildebrand, Houde).French : habitational name from any of several places in Normandy called La Houle or Les Houles, named in Old French with the singular or plural of houle ‘cave’.English : variant of Hole.
Surname or Lastname
English
English : variant of Mule.
Female
English
Variant spelling of Middle English Mauld, MOULD means "mighty in battle."
Girl/Female
German, Greek, Hebrew
Rich; Harmonious; Song; I will Praise the Lord
Surname or Lastname
English
English : nickname for someone supposedly resembling a mole (the burrowing mammal), Middle English mol(le) (from Dutch or Low German mol), for example in having poor eyesight.English : nickname for someone with a prominent mole or blemish on the face, from Middle English mole (Old English mÄl).English : from an Old English masculine personal name, Moll.English : from Old Norse moli ‘crumb’, ‘grain’, possibly a nickname for a small man.French : metonymic occupational name for a knife grinder or a maker of whetstones, from a variant of meule ‘whetstone’, ‘grindstone’, ‘millstone’.Italian : variant of Mule.Slovenian : probably a nickname for a extremely religious man, from mole ‘zealot’, a derivative of moliti ‘to pray’.
Girl/Female
African, Australian, Nigerian
I am Grateful; Gratefulness
Girl/Female
Welsh
Tower.
Boy/Male
Arabic, Assamese, Indian, Muslim
Main; New
Boy/Male
Irish
Name of a saint.
Surname or Lastname
English
English : from a medieval personal name, perhaps Old English MÅ«l (from Old English mÅ«l ‘mule’, ‘halfbreed’). This was the name of a brother of Ceadwalla, King of Wessex (died 675), and is also found as a place name element. However, it may not have survived to the Conquest, and Domesday Book Mule, Mulo may instead represent Old Norse MÅ«li, which is probably from Old Norse mÅ«li ‘muzzle’, ‘snout’.English : nickname for a stubborn person or metonymic occupational name for a driver of pack animals, from Middle English mule ‘mule’ (Old English mÅ«l, reinforced by Old French mule, both from Latin mula ‘she-mule’).English : from the medieval female personal name Mulle, variant of Molle, a pet form of Mary (see Marie).French : nickname from mule ‘mule’ (see 2).Dutch : nickname for a gossip or someone with a large mouth, from Middle Dutch mule ‘mouth’, ‘snout’.Dutch : metonymic occupational name for a maker of slippers, from Middle Dutch mule ‘slipper’.Italian (also Mulé) : from the medieval nickname Mulé, Molé, from Arabic mawlÄ â€˜gentleman’, ‘lord’, ‘master’, m(a)uley ‘my lord’.Sicilian and southern Italian : status name, from Arabic mawlÄ â€˜master’, ‘owner’.
Girl/Female
Greek
Harmonious.
Boy/Male
American, British, English
Of the Valley
Surname or Lastname
English
English : from the Middle English female personal name Mau(l)d, a reduced form of the Norman name Mathilde, Matilda, composed of the Germanic elements maht ‘might’, ‘strength’ + hild ‘strife’, ‘battle’. The learned form Matilda was much less common in the Middle Ages than the vernacular forms Mahalt, Maud and the reduced pet form Till. The name was borne by the daughter of Henry I of England, who disputed the throne of England with her cousin Stephen for a number of years (1137–48). In Germany the popularity of the name in the Middle Ages was augmented by its being borne by a 10th-century saint, wife of Henry the Fowler and mother of Otto the Great.
Girl/Female
Norse
Fighting woman.
Girl/Female
French Teutonic American German
Wealthy.
Surname or Lastname
English
English : topographic name for someone who lived or worked at a particular large house, from Old English boðl, botl ‘dwelling house’, ‘hall’, or a habitational name for someone who came from a place named with this element, probably Bodle Street near Hailsham, Sussex.
MODULE MATHEMATICS
MODULE MATHEMATICS
Girl/Female
Indian
Empowering someone
Girl/Female
Indian
Beautiful
Boy/Male
Indian, Sanskrit
Lotus Footed
Boy/Male
Tamil
Ascetic
Boy/Male
Arabic, Parsi
Firm; Vigorous; Summer
Girl/Female
Christian, Finnish, French, German, Greek, Hebrew, Swedish
Sea of Bitterness; Rebellious or Bitter; Star of the Sea; Beloved
Girl/Female
Indian, Telugu
Beauty
Boy/Male
Afghan, American, Arabic, Assamese, Celebrity, Gujarati, Hindu, Indian, Kannada, Latin, Malayalam, Marathi, Parsi, Sanskrit, Sindhi, Tamil, Telugu
King; Noble; Old Civilisation; Related; From a High Race; Son of Arya; That which is Beyond Anyone's Strength; Leader; Belonging to the Aryans who Loves Flute; Brave Noble
Girl/Female
Hindu
Victory, Good character
Boy/Male
Gujarati, Indian, Tamil
God
MODULE MATHEMATICS
MODULE MATHEMATICS
MODULE MATHEMATICS
MODULE MATHEMATICS
MODULE MATHEMATICS
n.
To model; also, to modulate.
n.
A fixed part of a module. See Module.
a.
Of or pertaining to mode, modulation, module, or modius; as, modular arrangement; modular accent; modular measure.
v. t.
To form into a particular shape; to shape; to model; to fashion.
imp. & p. p.
of Model
n.
The size of some one part, as the diameter of semi-diameter of the base of a shaft, taken as a unit of measure by which the proportions of the other parts of the composition are regulated. Generally, for columns, the semi-diameter is taken, and divided into a certain number of parts, called minutes (see Minute), though often the diameter is taken, and any dimension is said to be so many modules and minutes in height, breadth, or projection.
a.
Having powers of self-motion, though unconscious; as, the motile spores of certain seaweeds.
v. t.
To plan or form after a pattern; to form in model; to form a model or pattern for; to shape; to mold; to fashion; as, to model a house or a government; to model an edifice according to the plan delineated.
a.
Suitable to be taken as a model or pattern; as, a model house; a model husband.
v. t.
See Coddle.
v. t.
To mix confusedly; to confuse; to make a mess of; as, to muddle matters; also, to perplex; to mystify.
a.
Producing motion; as, motile powers.
n.
A model or measure.
pl.
of Morula
v. t.
To mix; to mingle; to meddle.
a.
Changing in appearance and expression under the influence of the mind; as, mobile features.
n.
One who models; hence, a worker in plastic art.
pl.
of Modulus
a.
Equally distant from the extreme either of a number of things or of one thing; mean; medial; as, the middle house in a row; a middle rank or station in life; flowers of middle summer; men of middle age.
a.
Lower by a semitone; flat; as, E molle, that is, E flat.