# Semi-simple ring

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.