semisimple.
In any of several technical senses, decomposable into sub-objects that have a simple structure.
Meaning & usage
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.
In any of several technical senses, decomposable into sub-objects that have a simple structure. In which each submodule is a direct summand; equivalently, equal to a direct sum of simple submodules.
In any of several technical senses, decomposable into sub-objects that have a simple structure. Semisimple as a module over itself; equivalently, such that all (left) modules are semisimple.
In any of several technical senses, decomposable into sub-objects that have a simple structure. Semisimple as a module over itself; equivalently, such that all (left) modules are semisimple. Semiprimitive: having trivial Jacobson radical.
In any of several technical senses, decomposable into sub-objects that have a simple structure. For which every invariant subspace has an invariant complement, equivalent to the minimal polynomial being squarefree.
In any of several technical senses, decomposable into sub-objects that have a simple structure. Being a direct sum of simple Lie algebras.
In any of several technical senses, decomposable into sub-objects that have a simple structure. Being a direct sum of simple representations (also known as irreducible representations).
In any of several technical senses, decomposable into sub-objects that have a simple structure. Being a linear algebraic group whose radical of the identity component is trivial.
Where this word comes from
From semi- + simple.
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Definitions, grammatical labels, IPA, etymology and examples: Wiktionary contributors, extracted by Kaikki / Wiktextract. Adapted under CC BY-SA 4.0. Selected fields and authored examples are shown; third-party quotations and audio are omitted. See contributor history.
Last enriched 2026-09-10. Definitions are in English. Romanizations are shown when supplied by the source; syllable estimates are omitted for unsupported scripts.