# Answer to Question #17102 in Algebra for john.george.milnor

Question #17102

Let R be a semisimple ring. Show that any ideal of R is a sum of simple components of R.

Expert's answer

Let

*R*=*B*1*⊕**· · ·**⊕**Bn*, where the*Bi*’s are ideals of*R*. Then any left ideal (resp. ideal)*I*of*R*has the form*I*=*I*1*⊕**· · ·**⊕**In*where, for each*i, Ii*is a left ideal (resp. ideal) of the ring*Bi*. Thus statement follows directly from mentioned fact.
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