Semisimple
From Wikipedia, the free encyclopedia
(Redirected from Reductive)
In mathematics, the term semisimple is used in a number of related ways, within different subjects. The common theme is the idea of a decomposition into 'simple' parts, that fit together in the cleanest way (by direct sum).
- A semisimple module is one in which each submodule is a direct summand
- A semisimple algebra (or ring) is one that is semisimple as a module over itself
- A semisimple operator (or matrix) is one for which every invariant subspace has an invariant complement. This is equivalent to the minimal polynomial being square-free. Over an algebraically closed field it is equivalent to diagonalizable.
- A semisimple Lie algebra is a Lie algebra which is a direct sum of simple Lie algebras.
- A semisimple algebraic group is a linear algebraic group whose radical of the identity component is trivial
[edit] See also
 |
This disambiguation page lists mathematics articles associated with the same title. If an internal link led you here, you may wish to change the link to point directly to the intended article. |
