semisimple

Algebra, Category theory, Computing, Engineering, Mathematics, Natural sciences, Physical sciences, Sciences Of an abelian category, Of an algebraic structure Containing a collection of simple objects such that all objects in the category are direct sums of these simple objects.

Algebra, Mathematics, Sciences Of a module, Of an algebraic structure In which each submodule is a direct summand; equivalently, equal to a direct sum of simple submodules.

Algebra, Mathematics, Sciences Of an algebra or ring, Of an algebraic structure Semisimple as a module over itself; equivalently, such that all (left) modules are semisimple.

Algebra, Mathematics, Sciences Proscribed, Of a ring, Of an algebraic structure, Of an algebra or ring Semiprimitive: having trivial Jacobson radical.

Algebra, Linear algebra, Mathematics, Sciences Of an operator or matrix, Of an algebraic structure For which every invariant subspace has an invariant complement, equivalent to the minimal polynomial being squarefree.

Algebra, Mathematics, Sciences Of a Lie algebra, Of an algebraic structure Being a direct sum of simple Lie algebras.

Algebra, Mathematics, Sciences Of an algebraic structure Being a direct sum of simple representations (also known as irreducible representations).

Algebra, Group theory, Mathematics, Sciences Of an algebraic group, Of an algebraic structure Being a linear algebraic group whose radical of the identity component is trivial.