Flat module information

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

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...

situations Flatness (systems theory), a property of nonlinear dynamic systems Spectral flatness Flat intonation Flat module in abstract algebra Flat morphism...

Euclidean space Flat (matroids), a further generalization of flats from linear algebra to the context of matroids Flat module in ring theory Flat morphism in...

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...

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...

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...

free module is a module that has a basis, that is, a generating set consisting of linearly independent elements. Every vector space is a free module, but...

positions on the flat module, open the lid of the box, and then remove the cylinders from the box and place them in position on the flat module. It is possible...

module. Pure modules are complementary to flat modules and generalize Prüfer's notion of pure subgroups. While flat modules are those modules which leave...

Faithfully flat may refer to: Faithfully flat morphism, in the theory of schemes in algebraic geometry Faithfully flat module, for sequences in algebra...

a module. Countably generated module Flat module Invariant basis number "ac.commutative algebra – Existence of a minimal generating set of a module –...

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...

indicators, used to operate machinery Flat panel display, in (for example) laptops and mobile devices Solar panel, a flat module of photovoltaic solar cells Panel...

algebra, a flat cover of a module M over a ring is a surjective homomorphism from a flat module F to M that is in some sense minimal. Any module over a ring...

criterion for flatness gives conditions one can check to show flatness of a module. Given a commutative ring A, an ideal I and an A-module M, suppose either...

an ideal Hilbert's Nullstellensatz Flat module Flat map Flat map (ring theory) Projective module Injective module Cohen-Macaulay ring Gorenstein ring...

rational numbers. More generally, a module M over a ring R is said to be a cotorsion module if Ext1(F,M)=0 for all flat modules F. This is equivalent to the...

sometimes called the flat dimension as it is the shortest length of the resolution of the module by flat modules. The weak dimension of a module is, at most,...

This process can be performed by flat glass recyclers, since the shape and composition of a PV module is similar to flat glass used in the building and...

of R are flat. All left ideals of R are flat. Submodules of all right flat R-modules are flat. Submodules of all left flat R-modules are flat. (The mixture...

module is a G-module, with G being the Galois group of some extension of fields. The term Galois representation is frequently used when the G-module is...

theory of descent (faithfully flat descent). The term flat here comes from flat modules. There are several slightly different flat topologies, the most common...

general R-module M, the functor M ⊗R − is only right exact. If it is exact, M is called flat. If R is local, any finitely presented flat module is free...

module. flat 1.  A flat module is a module such that tensoring with it preserves exactness. 2.  A flat resolution is a resolution by flat modules. 3.  For...

results discovered by Joachim Lambek shows that a module is flat if and only if the associated character module is injective. The group ( Q / Z , + ) {\displaystyle...