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Answer to Question #17103 in Algebra for john.george.milnor

Question #17103
Let R be a semisimple ring. Show that any quotient ring of R is semisimple.
Expert's answer
Write R = R1 ×· · ·×Rr where the Ri’s are the simple components of R. Consider any quotient ring R/I of R. After a reindexing, we may assume that I = R1 ⊕· · ·⊕Rs for some s ≤ r. Therefore, R/I ∼ Rs+1 ×· · ·×Rr is a semisimple ring.

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