In algebra, the length of a module over a ring R {\displaystyle R} is a generalization of the dimension of a vector space which measures its size. page...

Module theory is the branch of mathematics in which modules are studied. This is a glossary of some terms of the subject. See also: Glossary of linear...

submodule generated by a non-zero element of M equals M. Simple modules form building blocks for the modules of finite length, and they are analogous...

class of 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...

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...

other notions of dimension. For the non-free case, this generalizes to the notion of the length of a module. The uniquely defined dimension of every connected...

context of modules arises from the fact that many naturally occurring modules are not semisimple, hence cannot be decomposed into a direct sum of simple...

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

A DIMM (Dual In-line Memory Module) is a popular type of memory module used in computers. It is a printed circuit board with one or both sides (front...

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...

is n) Length of a module, in abstract algebra Length of a polynomial, the sum of the magnitudes of the coefficients of a polynomial Length of a vector...

{\displaystyle W(k)} -length. The Dieudonné module functor in one direction is given by homomorphisms into the abelian sheaf C W {\displaystyle CW} of Witt co-vectors...

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...

The flag's length is twenty modules and the width, fourteen, translating into an aspect ratio of 10:7. The distance of the vertices of the yellow rhombus...

electric panels, or PV modules. Solar panels are usually arranged in groups called arrays or systems. A photovoltaic system consists of one or more solar panels...

denote a finite complex of free R-modules such that ⨁ i H i ( G ∙ ) {\displaystyle \bigoplus \nolimits _{i}H_{i}(G_{\bullet })} has finite length but is...

Concepts and theorems Composition series Length of a module Structure theorem for finitely generated modules over a principal ideal domain Homological dimension...

(EMP2). The CMP offers a high level of modularity with a choice of two track widths, three wheelbase lengths, three rear modules and the capability to...

{\displaystyle \ell _{R}(M)} denotes the length of the module M {\displaystyle M} , and we assume for the remainder of the article that ℓ R ( ( R / P ) ⊗ R...

Experiment Module (JEM), is a Japanese science module for the International Space Station (ISS) developed by JAXA. It is the largest single ISS module, and...

A vector space can be seen as a particular case of a matroid, and in the latter there is a well-defined notion of dimension. The length of a module and...

T-TRAK (all letters capitalized) is a modular model railroad system based on standards for module size, track placement, track interface, and electrical...

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 linear...

data within the same module) R_Pointer and P_Pointer would be the same. LEN records are used to declare the length of a module where it was not known...

glossary of ring theory and glossary of module theory. In this article, all rings are assumed to be commutative with identity 1. Contents:  !$@ A B C D E...

_{i}^{A}(A/I,A/J))} where length is the length of a module over a local ring, and Tor is the Tor functor. When V and W can be moved into a transverse position...

A hardware security module (HSM) is a physical computing device that safeguards and manages secrets (most importantly digital keys), and performs encryption...

a basic statement in abstract algebra. Suppose M is a module over some ring. If M is indecomposable and has finite length, then every endomorphism of...

In abstract algebra, a decomposition of a module is a way to write a module as a direct sum of modules. A type of a decomposition is often used to define...

low floor trams come in lengths of three or four modules, all of which are approximately the same length. Under each module lies a bogie; the low floor,...