adj ·Uncommon ·Advanced level

Definitions

Adjective

1. 1
   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. not-comparable
2. 2
   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. not-comparable
3. 3
   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. not-comparable
4. 4
   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. not-comparable, proscribed
5. 5
   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. not-comparable

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6. 6
   In any of several technical senses, decomposable into sub-objects that have a simple structure.; Being a direct sum of simple Lie algebras. not-comparable
7. 7
   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). not-comparable
8. 8
   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. not-comparable

Synonyms

All synonyms

jacobson semisimple

Example

More examples

"A module is said to be semisimple if it is the sum of simple submodules."

Etymology

From semi- + simple.

Related phrases

algebraic grouplie algebra

Data sourced from Wiktionary, WordNet, CMU, and other open linguistic databases. Updated March 2026.