integer module
1Module (mathematics) — For other uses, see Module (disambiguation). In abstract algebra, the concept of a module over a ring is a generalization of the notion of vector space, wherein the corresponding scalars are allowed to lie in an arbitrary ring. Modules also… …
2module — Synonyms and related words: Earth insertion, LEM, LM, apogee, article, attitude control rocket, ballistic capsule, burn, capsule, deep space ship, docking, docking maneuver, entity, ferry rocket, fuel ship, individual, injection, insertion,… …
3integer — Synonyms and related words: Gaussian integer, algebraic number, article, cardinal, cardinal number, cipher, collectivity, complex, complex number, defective number, digit, embodiment, entirety, entity, even number, figure, finite number, fraction …
4Finitely generated module — In mathematics, a finitely generated module is a module that has a finite generating set. Equivalently, it is a homomorphic image of a free module on finitely many generators. The kernel of this homomorphism need not be finitely generated (then… …
5Indecomposable module — In abstract algebra, a module is indecomposable if it is non zero and cannot be written as a direct sum of two non zero submodules.Indecomposable is a weaker notion than simple module:simple means no proper submodule N < M,while indecomposable… …
6Injective module — In mathematics, especially in the area of 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. Specifically, if Q is a submodule of some… …
7Quotient module — In abstract algebra, a branch of mathematics, given a module and a submodule, one can construct their quotient module. This construction, described below, is analogous to how one obtains the ring of integers modulo an integer n , see modular… …
8Algebraic integer — This article deals with the ring of complex numbers integral over Z. For the general notion of algebraic integer, see Integrality .In number theory, an algebraic integer is a complex number which is a root of some monic polynomial (leading… …
9Serial module — Chain ring redirects here. For the bicycle part, see Chainring. In abstract algebra, a uniserial module M is a module over a ring R, whose submodules are totally ordered by inclusion. This means simply that for any two submodules N1 and N2 of M,… …
10Length of a module — In abstract algebra, the length of a module is a measure of the module s size . It is defined as the length of the longest ascending chain of submodules and is a generalization of the concept of dimension for vector spaces. The modules with… …
