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

Question #17652

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

Expert's answer

Now suppose

*R*is a simplering which has a minimal left ideal. Then soc(*)*_{R}R*<>*0 and so soc(*) =*_{R}R*R*. This means that*is a semisimple module, so*_{R}R*R*is a semisimple ring.
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