semisimple (English, adj)
expansion: semisimple (not comparable)
Senses:
topics: algebra
category-theory
computing
engineering
mathematics
natural-sciences
physical-sciences
sciences
glosses: 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.
qualifier: most generally
tags: not-comparable
raw_tags: of an abelian category
of an algebraic structure
topics: algebra
mathematics
sciences
glosses: 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.
qualifier: module theory
tags: not-comparable
raw_tags: of a module
of an algebraic structure
topics: algebra
mathematics
sciences
glosses: 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.
qualifier: ring theory
tags: not-comparable
raw_tags: of an algebra or ring
of an algebraic structure
topics: algebra
mathematics
sciences
glosses: 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.
qualifier: ring theory
tags: not-comparable
proscribed
raw_tags: of a ring
of an algebraic structure
of an algebra or ring
topics: algebra
linear-algebra
mathematics
sciences
glosses: 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.
tags: not-comparable
raw_tags: of an operator or matrix
of an algebraic structure
topics: algebra
mathematics
sciences
glosses: In any of several technical senses, decomposable into sub-objects that have a simple structure.
Being a direct sum of simple Lie algebras.
qualifier: Lie theory
tags: not-comparable
raw_tags: of a Lie algebra
of an algebraic structure
topics: algebra
mathematics
sciences
glosses: 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).
qualifier: representation theory
tags: not-comparable
raw_tags: of a linear representation of a group or algebra
of an algebraic structure
topics: algebra
group-theory
mathematics
sciences
glosses: 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.
tags: not-comparable
raw_tags: of an algebraic group
of an algebraic structure
Forms: