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 _{R}R is a semisimple module, so *R *is a semisimple ring.

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