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)...

In mathematics, particularly in algebra, the class of projective modules enlarges the class of free modules (that is, modules with basis vectors) over...

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,...

hardware Multi-chip module, a modern technique that combines several complex computer chips into a single larger unit Module (mathematics) over a ring, a...

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...

In mathematics, a finitely generated module is a module that has a finite generating set. A finitely generated module over a ring R may also be called...

In mathematics, algebraically compact modules, also called pure-injective modules, are modules that have a certain "nice" property which allows the solution...

In mathematics, more specifically in ring theory, a cyclic module or monogenous module is a module over a ring that is generated by one element. The concept...

In mathematics, especially in the area of abstract algebra known as module theory, a semisimple module or completely reducible module is a type of module...

ISBN 0-226-42454-5, MR 0345945 Lam, Tsit Yuen (1999). Lectures on modules and rings. Graduate Texts in Mathematics. Vol. 189. Springer. ISBN 0-387-98428-3. Lam, Tsit...

subjects, mathematics has been assessed in a modular system since the introduction of Curriculum 2000, whereby each candidate must take six modules, with...

In mathematics, a topological module is a module over a topological ring such that scalar multiplication and addition are continuous. A topological vector...

mathematics, or advanced level math. A qualification in Further Mathematics involves studying both pure and applied modules. Whilst the pure modules (formerly...

on Mathematics. New York: Dover Books. ISBN 978-1-61427-304-2. OCLC 912495626. Lang, Serge (2002), "III. Modules, §6. The dual space and dual module",...

In mathematics, the annihilator of a subset S of a module over a ring is the ideal formed by the elements of the ring that give always zero when multiplied...

In mathematics, specifically in ring theory, the simple modules over a ring R are the (left or right) modules over R that are non-zero and have no non-zero...

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

and true mathematical assertions, but appear to be nonsense to people who do not have the required background. For example, "every free module is flat"...

In mathematics, in the theory of modules, the radical of a module is a component in the theory of structure and classification. It is a generalization...

In abstract algebra, a Noetherian module is a module that satisfies the ascending chain condition on its submodules, where the submodules are partially...

the definitions of basis, module, and free module. H. B. Williams, an electrophysiologist, wrote in 1927: Now mathematics is both a body of truth and...

In mathematics, particularly in algebra, the injective hull (or injective envelope) of a module is both the smallest injective module containing it and...

In mathematics, a Clifford module is a representation of a Clifford algebra. In general a Clifford algebra C is a central simple algebra over some field...

In mathematics, the tensor product of modules is a construction that allows arguments about bilinear maps (e.g. multiplication) to be carried out in terms...

In topology and related areas of mathematics, a neighbourhood (or neighborhood) is one of the basic concepts in a topological space. It is closely related...

In mathematics, especially in the area of abstract algebra known as module theory, a principal indecomposable module has many important relations to the...

In algebra, given a module and a submodule, one can construct their quotient module. This construction, described below, is very similar to that of a...

In mathematics, a 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...

In mathematics, the Jacquet module is a module used in the study of automorphic representations. The Jacquet functor is the functor that sends a linear...

In mathematics, a D-module is a module over a ring D of differential operators. The major interest of such D-modules is as an approach to the theory of...