symmetric monoidal (∞,1)-category of spectra
An associative unital algebra over a field is semisimple if its Jacobson radical is trivial.
If is finite-dimensional, this is equivalent to saying that is a finite product of finite-dimensional simple algebras.
By the Artin-Wedderburn theorem, any finite-dimensional simple algebra over is a matrix algebra with entries lying in some division algebra whose center is . So, every finite-dimensional semisimple algebra is a finite product of such matrix algebras.
Last revised on October 14, 2012 at 16:50:26. See the history of this page for a list of all contributions to it.