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...

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...

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...

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...

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...

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 Apollo command and service module (CSM) was one of two principal components of the United States Apollo spacecraft, used for the Apollo program, which...

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...

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

{\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...

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 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...

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...

(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...

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...

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...

flat modules include free modules, projective modules, and, over a principal ideal domain, torsion-free modules. Formally, a module M over a ring 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 hardware security module (HSM) is a physical computing device that safeguards and manages secrets (most importantly digital keys), and performs encryption...

_{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...

{\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...

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...

with varying lengths of 30, 42, 60, 80 and 110 mm. The codes for the M.2 module sizes contain both the width and length of a particular module; for example...

pinyin: Tiānhé; lit. 'Harmony of the Heavens'), officially the Tianhe core module (Chinese: 天和核心舱), is the first module to launch of the Tiangong space station...

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...

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...

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,...

The Apollo Lunar Module (LM /ˈlɛm/), originally designated the Lunar Excursion Module (LEM), was the lunar lander spacecraft that was flown between lunar...

included a module which would be attached to Freedom, and with the capability to evolve into a full-fledged European orbital outpost before the end of the...