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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