semisimple
Containing a collection of simple objects such that all objects in the category are…In any of several technical senses, decomposable into sub-objects that have a simple structure.: Containing a collection of simple objects such that all objects in the category are direct sums of these simple objects.
» A module is said to be semisimple if it is the sum of simple submodules.
Ein Modul heißt halbeinfach, wenn er die Summe einfacher Untermoduln ist.
Модуль называется вполне приводимым, если он разлагается в прямую сумму неприводимых подмодулей.
Модуль называется полупростым, если он разлагается в прямую сумму простых подмодулей.
Meaning
8 sensesIn any of several technical senses, decomposable into sub-objects that have a simple structure.
(not comparable)Containing a collection of simple objects such that all objects in the category are direct sums of these simple objects.
(not comparable)In which each submodule is a direct summand; equivalently, equal to a direct sum of simple submodules.
(not comparable)Semisimple as a module over itself; equivalently, such that all (left) modules are semisimple.
Semisimple as a module over itself; equivalently, such that all (left) modules are semisimple.
(not comparable, proscribed)Semiprimitive: having trivial Jacobson radical.
In any of several technical senses, decomposable into sub-objects that have a simple structure.
(not comparable)For which every invariant subspace has an invariant complement, equivalent to the minimal polynomial being squarefree.
(not comparable)Being a direct sum of simple Lie algebras.
(not comparable)Being a direct sum of simple representations (also known as irreducible representations).
(not comparable)Being a linear algebraic group whose radical of the identity component is trivial.
Examples
1 sentencesA module is said to be semisimple if it is the sum of simple submodules.
ruМодуль называется вполне приводимым, если он разлагается в прямую сумму неприводимых подмодулей.
deEin Modul heißt halbeinfach, wenn er die Summe einfacher Untermoduln ist.
Origin
From semi- + simple.From semi- + simple.
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