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Definition of Semisimple
1. Adjective. (mathematics of a module) In which each submodule is a direct summand. ¹
2. Adjective. (mathematics of an algebra or ring) ¹
3. Adjective. (mathematics of an operator or matrix) For which every invariant subspace has an invariant complement, equivalent to the minimal polynomial being squarefree. ¹
4. Adjective. (mathematics of a Lie algebra) Being a direct sum of simple Lie algebras. ¹
5. Adjective. (mathematics of an algebraic group) Being a linear algebraic group whose radical of the identity component is trivial. ¹
¹ Source: wiktionary.com
Lexicographical Neighbors of Semisimple
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