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...

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...

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

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

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...

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...

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...

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

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 the...

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...

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

"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...

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

module. Over a commutative ring R with total quotient ring K, a module M is torsion-free if and only if Tor1(K/R,M) vanishes. Therefore flat modules,...

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...

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...

is an element of a module that yields zero when multiplied by some non-zero-divisor of the ring. The torsion submodule of a module is the submodule formed...

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

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,...

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...

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. 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...

instance, 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...

the homology is of the complexes formed by tensor product with C (some flat module condition should enter). The construction of β is by the usual argument...

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...

-\otimes _{R}F} is exact. In particular, every projective module is flat. free A free module is a module that has a basis, or equivalently, one that is isomorphic...

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...