simple modules over a ring R are the (left or right) modules over R that are non-zero and have no non-zero proper submodules. Equivalently, a module M...

R-modules preserves exactness. Torsionless A module is called torsionless if it embeds into its algebraic dual. Simple A simple module S is a module that...

Indecomposable is a weaker notion than simple module (which is also sometimes called irreducible module): simple means "no proper submodule" N < M, while...

area of abstract algebra known as module theory, a semisimple module or completely reducible module is a type of module that can be understood easily from...

trivial module 0 is semi-simple, but not simple). For an R-module M, M is semi-simple if and only if it is the direct sum of simple modules (the trivial...

structure, such as a group or a module, into simple pieces. The need for considering composition series in the context of modules arises from the fact that...

A/0 Modules/Async/A Modules/AsynchronousDefinition Modules/LoaderPlugin Modules/Resources Modules/SimpleAsynchronous Modules/Transport/B,C,D,E Modules/Wrappings...

panels are also known as solar cell panels, solar electric panels, or PV modules. Solar panels are usually arranged in groups called arrays or systems....

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...

led to the creation of the Whitehead manifold. The definition of crossed modules is due to him. He also made important contributions in differential topology...

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 modules. Various...

a graphics module for simple hardware acceleration of 2D computer graphics which includes text rendering using FreeType, an audio module that uses OpenAL...

R-module N is cyclic if N = yR for some y ∈ N. 2Z as a Z-module is a cyclic module. In fact, every cyclic group is a cyclic Z-module. Every simple R-module...

module version of Schur's lemma admits generalizations involving modules M that are not necessarily simple. They express relations between the module-theoretic...

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...

Rn by a particularly simple submodule, and this is the structure theorem. The structure theorem for finitely generated modules over a principal ideal...

Simple Network Management Protocol (SNMP) is an Internet Standard protocol for collecting and organizing information about managed devices on IP networks...

algebra, a module homomorphism is a function between modules that preserves the module structures. Explicitly, if M and N are left modules over a ring...

algebra, an Artinian module is a module that satisfies the descending chain condition on its poset of submodules. They are for modules what Artinian rings...

example, a semisimple module is a module that has a decomposition into simple modules. Given a ring, the types of decomposition of modules over the ring can...

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...

A semisimple module is a direct sum of simple modules. A semisimple ring is a ring that is semisimple as a left module (or right module) over itself....

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

(7400-series) capable of running simple programs such as computing the Fibonacci sequence. Eater's design consists of the following modules: An adjustable-speed (upper...

the number of simple modules k(G) is equal to the number of conjugacy classes of G. In the modular case, the number l(G) of simple modules is equal to the...

as module theory, a principal indecomposable module has many important relations to the study of a ring's modules, especially its simple modules, projective...

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...

intersection theory. The zero module is the only one with length 0. Modules with length 1 are precisely the simple modules. The length of the cyclic group...

isomorphism) simple highest-weight g {\displaystyle {\mathfrak {g}}} -module with highest weight λ, which is denoted L(λ), but this module is infinite...

ESP-01 module, made by a third-party manufacturer Ai-Thinker. This small module allows microcontrollers to connect to a Wi-Fi network and make simple TCP/IP...