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...

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...

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...

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...

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)...

algebra, flat modules include free modules, projective modules, and, over a principal ideal domain, torsion-free modules. Formally, a module M over a ring...

equivalently be called free Z {\displaystyle \mathbb {Z} } -modules, the free modules over the integers. Lattice theory studies free abelian subgroups of...

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...

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...

ring is commutative). A torsion module is a module consisting entirely of torsion elements. A module is torsion-free if its only torsion element is the...

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...

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...

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...

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...

A persistence module is a mathematical structure in persistent homology and topological data analysis that formally captures the persistence of topological...

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...

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....

resolutions consisting, respectively of free modules, projective modules or flat modules. Similarly every module has injective resolutions, which are right...

field or a free module over a ring in representation theory, but can also be used as a synonym for G-module. The study of Galois modules for extensions...

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...

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...

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...

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...

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...

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...

Free object Free abelian group Free algebra Free group Free module Free semigroup Free variable Free (surname) Free (rapper) (born 1968), or Free Marie...

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...

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...

loadable module (kld) in FreeBSD, kernel extension (kext) in macOS (although support for third-party modules is being dropped), kernel extension module in AIX...

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...