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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, but, if
Free_module
Module over a ring
In algebra, a torsion-free module is a module over a ring such that zero is the only element annihilated by a regular element (non zero-divisor) of the
Torsion-free_module
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 generated module F over
Stably_free_module
Direct summand of a free module (mathematics)
projective modules enlarges the class of free modules (that is, modules with basis vectors) over a ring, keeping some of the main properties of free modules. Various
Projective_module
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)
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
Algebra of formal sums
equivalently be called free Z {\displaystyle \mathbb {Z} } -modules, the free modules over the integers. Lattice theory studies free abelian subgroups of
Free_abelian_group
Topics referred to by the same term
Look up module or modular in Wiktionary, the free dictionary. Module, modular and modularity may refer to the concept of modularity. They may also refer
Module
A persistence module is a mathematical structure in persistent homology and topological data analysis that formally captures the persistence of topological
Persistence_module
In algebra, a module over a ring
In algebra, a free presentation of a module M over a commutative ring R is an exact sequence of R-modules: ⨁ i ∈ I R → f ⨁ j ∈ J R → g M → 0.
Free_presentation
Representation of an algebra as a free module
a representation of an algebra over a field as a finitely generated free module over a polynomial subalgebra or a regular local ring. Such decompositions
Hironaka_decomposition
Type of mathematical equation
finitely generated free K[x] module is also free. The construction of higher order syzygy modules is generalized as the definition of free resolutions, which
Linear_relation
Zero divisors in a module
is an integral domain). A torsion module is a module consisting entirely of torsion elements. A module is torsion-free if its only torsion element is the
Torsion_(algebra)
On polynomial rings over fields
that the nth syzygy module of a module M is free or projective. The above property of invariance, up to the sum direct with free modules, implies that n does
Hilbert's_syzygy_theorem
Mathematical terminology
the G-module is a vector space over a field or a free module over a ring in representation theory, but can also be used as a synonym for G-module. The
Galois_representation
In algebra, module with a finite generating set
generated module is a module that has a finite generating set. A finitely generated module over a ring R may also be called a finite R-module, finite over
Finitely_generated_module
modules is torsionless. A free module is reflexive if it is finitely generated, and for some rings there are also infinitely generated free modules that
Torsionless_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
Exact sequence used to describe the structure of an object
resolutions consisting, respectively of free modules, projective modules or flat modules. Similarly every module has injective resolutions, which are right
Resolution_(algebra)
Set of finitely supported functions from a group to a ring
ring is a free module and at the same time a ring, constructed in a natural way from any given ring and any given group. As a free module, its ring of
Group_ring
Statement in abstract algebra
the resulting indecomposable module is R {\displaystyle R} itself, and this is inside the part of M that is a free module. The summands R / ( q i ) {\displaystyle
Structure theorem for finitely generated modules over a principal ideal domain
Structure_theorem_for_finitely_generated_modules_over_a_principal_ideal_domain
Concept in mathematics
e.g. M itself, this shows that a module is a quotient of a free module, a useful fact.) A generating set of a module is said to be minimal if no proper
Generating_set_of_a_module
geometry. Formally, a finitely generated module M over a ring R is said to be invertible if it is locally a free module of rank 1. In other words, M P ≅ R P
Invertible_module
Dynamically loadable module that extends a running operating system kernel
loadable module (kld) in FreeBSD, kernel extension (kext) in macOS (although support for third-party modules is being dropped), kernel extension module in AIX
Loadable_kernel_module
finitely generated free modules. 2. A finitely presented module is a module that admits a finite free presentation. finitely generated A module M {\displaystyle
Glossary_of_module_theory
"Smallest" commutative algebra that contains a vector space
definitions and properties extend naturally to the case where V is a module (not necessarily a free one) over a commutative ring. It is possible to use the tensor
Symmetric_algebra
Commutative algebra theorem
commutative algebra concerning the relationship between free modules and projective modules over polynomial rings. In the geometric setting it is a statement
Quillen–Suslin_theorem
Basis of polynomials consisting of monomials
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 all monomials
Monomial_basis
Set of vectors used to define coordinates
every module has a basis. A module that has a basis is called a free module. Free modules play a fundamental role in module theory, as they may be used
Basis_(linear_algebra)
Topics referred to by the same term
object Free abelian group Free algebra Free group Free module Free semigroup Free variable Free (surname) Free (rapper) (born 1968), or Free Marie, American
Free
module has an associated character module. Using the associated character module it is possible to investigate the properties of the original module.
Character_module
Category whose objects are R-modules and whose morphisms are module homomorphisms
Stable module category Eilenberg–Watts theorem "module category in nLab". ncatlab.org. trivially since any module is a quotient of a free module. Dummit
Category_of_modules
{Ber} (X)\mathrm {Ber} (Y)} The determinant of an endomorphism of a free module M can be defined as the induced action on the 1-dimensional highest exterior
Berezinian
Mathematical object in abstract algebra
abstract algebra known as module theory, an injective module is a module Q that shares certain desirable properties with the Z-module Q of all rational numbers
Injective_module
Algebraic structure associated with a topological space
covariant additive functor F and some module X. The chain complex for X is defined as follows: first find a free module F 1 {\displaystyle F_{1}} and a surjective
Homology_(mathematics)
Topics referred to by the same term
mathematics, torsion-free may refer to: Torsion-free group, a group whose only element of finite order is the identity Torsion-free module, module over an integral
Torsion-free
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
Cohen–Macaulay_ring
Matrix normal form
working with finitely generated modules over a PID, and in particular for deducing the structure of a quotient of a free module. It is named after the Irish
Smith_normal_form
Algebraic structure with addition and multiplication
module over a semisimple ring is semisimple. (Proof: A free module over a semisimple ring is semisimple and any module is a quotient of a free module
Ring_(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
Position in a hierarchy
maximal linearly independent subset Rank of an elliptic curve Rank of a free module Rank of a generalized eigenvector Rank of a greedoid, the maximal size
Rank
Mathematical theorem
invariants K[V]G is a (free) polynomial algebra. (B') The algebra of invariants K[V]G is a regular ring. (C) The algebra K[V] is a free module over K[V]G. (C')
Chevalley–Shephard–Todd theorem
Chevalley–Shephard–Todd_theorem
over a field F (of characteristic not 2) with coefficients in Z/2Z is a free module over the cohomology ring of F with a basis 1, f3, f5, of degrees 0, 3
Albert_algebra
Component of the Apollo spacecraft
The Apollo command and service module (CSM) was one of two principal components of the United States Apollo spacecraft, used for the Apollo program, which
Apollo command and service module
Apollo_command_and_service_module
Operation that pairs a left and a right R-module into an abelian group
of modules is a construction that allows arguments about bilinear maps (e.g. multiplication) to be carried out in terms of linear maps. The module construction
Tensor_product_of_modules
Form of written communication for math
without some prerequisite knowledge. For example, the sentence "a free module is a module that has a basis" is perfectly correct, although it may appear
Language_of_mathematics
Free object in the category of associative algebras
a free commutative algebra. For R a commutative ring, the free (associative, unital) algebra on n indeterminates {X1,...,Xn} is the free R-module with
Free_algebra
Structure-preserving map between two algebraic structures of the same type
The endomorphisms of a vector space or of a module form a ring. In the case of a vector space or a free module of finite dimension, the choice of a basis
Homomorphism
Vector space equipped with a bilinear product
unital zero algebra over a free R-module allows extending this theory as a Gröbner basis theory for submodules of a free module. This extension allows, for
Algebra_over_a_field
the invariant basis number (IBN) property if all finitely generated free modules over R have a well-defined rank. In the case of fields, the IBN property
Invariant_basis_number
Algebraic structure
module over K[X] may be decomposed into a direct sum of a free module and finitely many modules of the form K [ X ] / ⟨ P k ⟩ {\displaystyle K[X]/\left\langle
Polynomial_ring
Assembly of photovoltaic cells used to generate electricity
device that converts sunlight into electricity by using multiple solar modules that consist of photovoltaic (PV) cells. PV cells are made of materials
Solar_panel
Algebraic structure
R} ). If M is a free module over a principal ideal domain R, then every submodule of M is again free. This does not hold for modules over arbitrary rings
Principal_ideal_domain
Algebraic structure
independents. A module that has a basis is called a free module, and a submodule of a free module needs not to be free. A module of finite type is a module that
Commutative_ring
Branch of mathematics
modules, even if one restricts oneself to finitely generated modules. However, every module is a cokernel of a homomorphism of free modules. Modules over
Linear_algebra
algebra of a finite-dimensional G-module. Then G is a reflection group if and only if S {\displaystyle S} is a free module (of finite rank) over SG (Chevalley's
Fixed-point_subring
adopt this convention in this article. Any finitely-generated torsion-free module M over R can be considered as a full R-lattice by taking as the ambient
Lattice_(module)
Conjecture in algebraic geometry
coordinate ring R. This conjecture states that if the derivations of R are a free module over R, then V is smooth. Nakai, Yoshikazu (1961), "On the theory of
Nakai_conjecture
Topics referred to by the same term
writing a finitely generated module over a principal ideal domain as the direct sum of cyclic modules and one free module. This disambiguation page lists
Cycle_decomposition
Polynomial whose Laplacian is zero
polynomial. This is equivalent to the statement that the polynomial ring is a free module over the ring of radial polynomials. Consider a degree- d {\displaystyle
Harmonic_polynomial
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
Abstract algebra concept
decomposition of a module is a way to write a module as a direct sum of modules. A type of a decomposition is often used to define or characterize modules: for example
Decomposition_of_a_module
Linux kernel framework
Dynamic Kernel Module Support (DKMS) is a program/framework that enables generating Linux kernel modules whose sources generally reside outside the kernel
Dynamic_Kernel_Module_Support
Kaplansky's theorem on projective modules, first proven by Irving Kaplansky, states that a projective module over a local ring is free; where a not-necessarily-commutative
Kaplansky's theorem on projective modules
Kaplansky's_theorem_on_projective_modules
Sheaf cohomology on the étale site
is a free module of rank 2 over the integers, while the first ℓ-adic cohomology group of an elliptic curve over a finite field is a free module of rank
Étale_cohomology
Bourbaki ideal of a torsion-free module M is an ideal isomorphic (as a module) to a torsion-free quotient of M by a free submodule. Buchsbaum ring A Buchsbaum
Glossary of commutative algebra
Glossary_of_commutative_algebra
Left adjoint to a forgetful functor to sets
free Lie algebra free magma free module, and in particular, vector space free monoid free commutative monoid free partially commutative monoid free ring
Free_object
Construction in homological algebra
H^{0}(K_{s})=A/(s_{1},\dots ,s_{r})} . Let R be a commutative ring and E a free module of finite rank r over R. We write ⋀ i E {\displaystyle \bigwedge ^{i}E}
Koszul_complex
Method of proof involving paradoxical properties of infinite sums
R} then there is a free module F {\displaystyle F} with A ⊕ F ≅ F {\displaystyle A\oplus F\cong F} . To see this, choose a module B {\displaystyle B}
Eilenberg–Mazur_swindle
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
Number of independent parameters of a system
(statistics), the number of values in the final calculation of a statistic that are free to vary Degrees of freedom problem, the problem of controlling motor movement
Degrees_of_freedom
the field of ring theory, a (right) free ideal ring, or fir, is a ring in which all right ideals are free modules with unique rank. A ring such that all
Free_ideal_ring
Prime ideal that is an annihilator of a prime submodule
In abstract algebra, an associated prime of a module M over a ring R is a type of prime ideal of R that arises as an annihilator of a (prime) submodule
Associated_prime
Types of mappings in mathematics
be a free module over a commutative ring A. We view A as a free module of rank 1 over itself. By the dual module E∨ of E we shall mean the module Hom(E
Functional_(mathematics)
Property of a mathematical space
other notions of dimension. For the non-free case, this generalizes to the notion of the length of a module. The uniquely defined dimension of every
Dimension
In mathematics, a supermodule is a Z2-graded module over a superring or superalgebra. Supermodules arise in super linear algebra which is a mathematical
Supermodule
Japanese ISS module, used on ISS press conferences
きぼう; lit. 'Hope'), also known as the Japanese Experiment Module (JEM), is a Japanese science module for the International Space Station (ISS) developed by
Kibō_(ISS_module)
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
2008 video game
products: DCS World, Modules, and Campaigns. DCS World is a free-to-play game that includes two free aircraft and two free maps. Modules are paid downloadable
Digital_Combat_Simulator
Concept in linear algebra
to a bilinear form on a free module over a commutative ring, and to a sesquilinear form extended to include any free module over a commutative ring with
Orthogonal_complement
Free and open-source 3D CAD software
add building information modeling (BIM) functionality with the Arch Module. FreeCAD has a modular structure built from a set of workbenches, where basic
FreeCAD
Topics referred to by the same term
derived functors of the tensor product of modules over a ring Torsion-free module, in algebra See also Torsion-free (disambiguation) Analytic torsion (Reidemeister
Torsion
Generalization of vector bundles
free O X {\displaystyle {\mathcal {O}}_{X}} -modules (sheaves of dual sections). But there may be an O X {\displaystyle {\mathcal {O}}_{X}} -module homomorphism
Coherent_sheaf
Basis of a type of algebraic structure
the precise context: In a coordinate space, and more generally in a free module, it refers to the standard basis defined by the Kronecker delta. In a
Canonical_basis
free resolutions of R as graded module over K[X0, X1, X2, ..., XN]. A resolution is defined as minimal if the image in each module morphism of free modules
Homogeneous_coordinate_ring
Series of spacecraft designed for the Soviet space programme
of three main sections. The descent module is where cosmonauts are seated for launch and reentry. The orbital module provides additional living space and
Soyuz_(spacecraft)
Apache module
domains on the same server. Free and open-source software portal List of Apache modules "FreshPorts -- www/mod_mono: Apache module for serving ASP.NET applications"
Mod_mono
Ring that is also a vector space or a module
R-algebra to its underlying ring (forgetting the module structure). See also: Change of rings. Free algebra A free algebra is an algebra generated by symbols
Associative_algebra
Electronics module
“potential-free” hybrid power module. It was available in a variety of connection layouts using both diodes and thyristors. “Potential-free” meant that
Power_module
Branch of mathematics that studies algebraic structures
a module Radical of a module Free module Quotient module Direct sum, Direct product of modules Direct limit, Inverse limit Localization of a module Completion
List of abstract algebra topics
List_of_abstract_algebra_topics
Compartment in space capsules used only in orbit
module has been upgraded to carry its own solar panels and orbital maneuver system, so it is capable of operating independently as an uncrewed free-flying
Orbital_module
First module of the International Space Station
блок), is the first module of the International Space Station (ISS). Launched on 20 November 1998 atop a Proton-K rocket, the module would serve as the
Zarya_(ISS_module)
covariants of binary forms Hermite ring, a ring over which every stably free module is free of unique rank Hermite-Sobolev spaces Hermite's cotangent identity
List of things named after Charles Hermite
List_of_things_named_after_Charles_Hermite
or algebra with straightening law is a commutative algebra that is a free module over some ring R, together with a given basis similar to the basis of
Hodge_algebra
Hewlett-Packard handheld RPN calculator
in a single module, thus freeing two expansion slots. HP designed a module holding all four in one slot, the so-called Quad Memory Module. The later HP-41CV
HP-41C
being a flat module over a commutative ring is a local property, but being a free module is not. For more, see Localization of a module. Local path connectedness
Local_property
Web content management system
free modules that extend and customize Drupal functionality, over 3,000 free themes that change the look and feel of Drupal, and at least 1,400 free distributions
Drupal
Concept in category theory
adjoint of the forgetful functor from the category of rings to Set; i.e., free module functor. Then F U {\displaystyle FU} defines a cotriple and the n-th
Cotriple_homology
Algebraic structure also called skew field
are the only rings over which every module is free: a ring R is a division ring if and only if every R-module is free. The center of a division ring is
Division_ring
travel, tourism, insurance
FREE MODULE
FREE MODULE
Surname or Lastname
English
English : variant of Freer 1.French (Frère) : from frère ‘brother’, used as a byname for the younger of two brothers.
Male
Swedish
Danish and Swedish form of Old Norse Freyr, FREJ means "lord, master."
Surname or Lastname
English (mainly southeastern)
English (mainly southeastern) : topographic name for someone who lived near a conspicuous tree, Middle English tre(w).
Boy/Male
English Norse Scandinavian
Lord.
Boy/Male
British, English
Peace
Boy/Male
Australian, British, English
In Liberty
Surname or Lastname
English
English : variant spelling of Fry.North German : variant of Frey.Joseph Frye (1711/12–94) was a military officer from Andover, MA, where the family had long been of local prominence. In 1762, he was granted a township in ME, later named Fryeburg after him, and moved his family there. His great-great-grandson William Pierce Frye was born in Lewiston, ME, and served in Congress, first as a member of the House of Representatives and then the Senate from 1871 until his death in 1911.
Male
English
Short form of English Frederick, FRED means "peaceful ruler."
Male
Icelandic
Icelandic form of Old Norse Freyr, FREY means "lord, master."
Boy/Male
English American Teutonic German
Sage, wise. From the Old English Aelfraed, meaning elf counsel. Also from Ealdfrith or Alfrid,...
Boy/Male
Anglo, British, English
Foreign
Boy/Male
British, English
Seed
Girl/Female
Irish American
Hill. Also abbreviation of Brina and Breanna.
Female
English
Anglicized form of Danish Freya, FREA means "lady, mistress."
Surname or Lastname
English
English : from Old French and Middle English frere ‘friar’ (Latin frater, literally ‘brother’). This was a status name for a member a religious order, especially a mendicant order, and may also have been a nickname for a pious person or for someone employed at a monastery.Americanized spelling of French Frère (see Frere).North German and Dutch : cognate of Friedrich.
Boy/Male
German, Swedish
Lord
Surname or Lastname
English (chiefly East Anglia)
English (chiefly East Anglia) : nickname or status name from Old English frēo ‘free(-born)’, i.e. not a serf.North German : topographic or habitational name from a place named Frede or Frede(n).North German : nickname from a variant of Middle Low German wrēd ‘crooked’.
Surname or Lastname
English
English : nickname from Middle English freil, frel(i)e ‘frail’, ‘weak’.Possibly an Americanized spelling of German Friel 2.
Boy/Male
British, English
Generous
Female
English
English form of Irish BrÃgh, BREE means "force, strength."
FREE MODULE
FREE MODULE
FREE MODULE
FREE MODULE
FREE MODULE
FREE MODULE
FREE MODULE
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