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...

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...

separate modules for different functions. The modules can be connected together by the user to create a patch. The outputs from the modules may include...

simple g {\displaystyle {\mathfrak {g}}} -module V μ {\displaystyle V^{\mu }} having μ {\displaystyle \mu } as its highest weight and (2) two simple modules...

non-zero module over a left semi-Artinian ring, then soc(M) is itself an essential submodule of M. This is because any non-zero module over a left semi-Artinian...

simple subalgebras. The Jacobson radical of an algebra over a field is the ideal consisting of all elements that annihilate every simple left-module....

must be protected from mechanical damage and moisture. Most modules are rigid, but semi-flexible ones based on thin-film cells are also available. The...

simple submodule (the socle) of the Schur module ∇(λ), but it need not be equal to the Schur module. The dimension and character of the Schur module are...

MR 1314422 Bourbaki, Nicolas (2012). Algèbre. Chapitre 8, Modules et anneaux semi-simples. Heidelberg: Springer-Verlag Berlin Heidelberg. ISBN 978-3-540-35315-7...

categories found in nature. For example, most module categories over a ring R {\displaystyle R} are not semi-simple; in fact, this is the case if and only if...

play a crucial role in electric vehicles, high-brightness LEDs and power modules, among other applications. Semiconductors have large thermoelectric power...

{g}}W} is simple (resp. absolutely simple), then W is simple (resp. absolutely simple). Here, a g {\displaystyle {\mathfrak {g}}} -module V is absolutely...

station’s vast system of solar panels and radiators to its pressurized modules. These modules support diverse functions, including scientific research, crew habitation...

Analytics: This module offers predictive analytics. Process: Implementation of Hayes' popular SPSS PROCESS module for JASP Prophet: A simple model for time...

associated its head, P/JP, which is a simple module, being an indecomposable semi-simple module. To each simple module S is associated its projective cover...

A semi-trailer truck (also known by a wide variety of other terms – see below) is the combination of a tractor unit and one or more semi-trailers to carry...

Localization of a module Completion (ring theory) Types Simple module, Semisimple module Indecomposable module Artinian module, Noetherian module Homological...

finite simple abelian groups are exactly the cyclic groups of prime order.: 32  The concepts of abelian group and Z {\displaystyle \mathbb {Z} } -module agree...

the ideal consisting of those elements in R that annihilate all simple right R-modules. It happens that substituting "left" in place of "right" in the...

non-trivial two-sided ideals is called quasi-simple. Rings which are simple as rings but are not a simple module over themselves do exist: a full matrix ring...

left (right) Loewy ring or left (right) semi-Artinian ring is a ring in which every non-zero left (right) module has a non-zero socle, or equivalently if...

The working draft for the level 4 color module combines the Basic and Extended sections together in a simple "Named Colors" section. CSS 2, SVG and CSS...

A transmission control unit (TCU), also known as a transmission control module (TCM), or a gearbox control unit (GCU), is a type of automotive ECU that...

eiRei a local ring. Every simple left (right) R-module has a projective cover. Every finitely generated left (right) R-module has a projective cover. The...

ISSN 0002-9947, MR 0260794 Bourbaki, Nicolas (1973), Algébre, Ch. 8: Modules et Anneaux Semi-Simples, p. 50, ISBN 978-2-7056-1261-0 Camillo, V. P.; Fuller, K. R...

An AR-15–style rifle is a lightweight semi-automatic rifle based on or similar to the Colt AR-15 design. The Colt model removed the selective fire feature...

Chevalley and Samuel Eilenberg (1948) to coefficients in an arbitrary Lie module. If G {\displaystyle G} is a compact simply connected Lie group, then it...

of simple artinian rings given by Artin–Wedderburn theory. To see the equivalence, notice that if X is a left R-module then Xn is an Mn(R)-module where...

The category of such modules is semisimple, so every module is a direct sum of simple modules. The simple modules are the modules E s / r {\displaystyle...

on) KEEL module for semi-supervised learning. Semi-Supervised Learning Software Semi-Supervised learning — scikit-learn documentation Semi-supervised...