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...

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)...

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...

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...

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...

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...

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...

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

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...

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...

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...

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...

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

left modules over R is the category whose objects are all left modules over R and whose morphisms are all module homomorphisms between left R-modules. For...

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...

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...

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...

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...

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

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...

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...

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

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

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...

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....

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...

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...