# Semi-simple ring

From Encyclopedia of Mathematics

A ring $A$ with zero radical. More precisely, if $\mathcal{R}$ is some radical (see Radical of rings and algebras), then the ring $A$ is called $\mathcal{R}$-semi-simple if $\mathcal{R}(A) = 0$. Frequently, by an associative semi-simple ring one understands a classical semi-simple ring.

**How to Cite This Entry:**

Semi-simple ring.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Semi-simple_ring&oldid=33973

This article was adapted from an original article by L.A. Skornyakov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article