basis of module
1Basis (linear algebra) — Basis vector redirects here. For basis vector in the context of crystals, see crystal structure. For a more general concept in physics, see frame of reference. In linear algebra, a basis is a set of linearly independent vectors that, in a linear… …
2Module (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… …
3Module libre — En algèbre, un module libre est un module M qui possède une base B, c est à dire un sous ensemble de M tel que tout élément de M s écrive de façon unique comme combinaison linéaire (finie) d éléments de B. Sommaire 1 Définitions 2 Exemples et… …
4module — /moj oohl/, n. 1. a separable component, frequently one that is interchangeable with others, for assembly into units of differing size, complexity, or function. 2. any of the individual, self contained segments of a spacecraft, designed to… …
5module — /ˈmɒdʒul / (say mojoohl) noun 1. a standard or unit for measuring. 2. a selected unit of measure, ranging in size from a few inches to several feet, used as a basis for planning and standardisation of building materials. 3. a structural component …
6module — mod•ule [[t]ˈmɒdʒ ul[/t]] n. 1) a separable component, frequently one that is interchangeable with others, for assembly into units of differing size, complexity, or function 2) ars any of the self contained segments of a spacecraft 3) wam a… …
7Free module — In mathematics, a free module is a free object in the category of modules. Given a set S , a free module on S is a (particular construction of a) free module with basis S .Every vector space is free, and the free vector space on a set is a… …
8Injective 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… …
9Galois module — In mathematics, a Galois module is a G module where G is the Galois group of some extension of fields. The term Galois representation is frequently used when the G module is a vector space over a field or a free module over a ring, but can also… …
10Projective module — In mathematics, particularly in abstract algebra and homological algebra, the concept of projective module over a ring R is a more flexible generalisation of the idea of a free module (that is, a module with basis vectors). Various equivalent… …
