semisimple

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adjective

Containing a collection of simple objects such that all objects in the category are direct sums of these simple objects.

Similar
Jacobson semisimple
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Meanings

adjectivesemisimple (not comparable)
  1. In any of several technical senses, decomposable into sub-objects that have a simple structure.
    1. not comparablemost generallyalgebraContaining a collection of simple objects such that all objects in the category are direct sums of these simple objects.
    2. not comparablemodule theoryalgebraIn which each submodule is a direct summand; equivalently, equal to a direct sum of simple submodules.
    3. not comparablering theoryalgebraSemisimple as a module over itself; equivalently, such that all (left) modules are semisimple.
    4. not comparableproscribedring theoryalgebraSemiprimitive: having trivial Jacobson radical.

      Synonyms: Jacobson semisimple

    5. not comparablealgebraFor which every invariant subspace has an invariant complement, equivalent to the minimal polynomial being squarefree.
    6. not comparableLie theoryalgebraBeing a direct sum of simple Lie algebras.
    7. not comparablerepresentation theoryalgebraBeing a direct sum of simple representations (also known as irreducible representations).
    8. not comparablealgebraBeing a linear algebraic group whose radical of the identity component is trivial.

Synonyms & antonyms

adjectiveSemiprimitive: having trivial Jacobson radical.

Similar
Jacobson semisimple

Origin

From semi- + simple.

Full word history & related roots →
Cite this entry
APA

semisimple. (n.d.). In WatkinsX Dictionary. Retrieved November 3, 2026, from https://dictionary.watkinsx.com/word/semisimple

MLA

“semisimple.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/semisimple. Accessed November 3, 2026.

Chicago

WatkinsX Dictionary, s.v. “semisimple,” accessed November 3, 2026, https://dictionary.watkinsx.com/word/semisimple.

Source: semisimple on Wiktionary, CC BY-SA 4.0.