Answer to Question #17652 in Abstract Algebra for Hym@n B@ss

Question

Give proof for the fact that if R is a simple ring which has a minimal left ideal, then R is a semisimple ring.

Answer 1

Now suppose R is a simplering which has a minimal left ideal. Then soc(_RR) <>0 and so soc(_RR) = R. This means that _RR is a semisimple module, so R is a semisimple ring.