I know that if $A$ is semisimple, then every $A$-module is semisimple. But I don't know how to prove then that a short exact sequence $$0 \to L \to M \to N \to 0$$ splits for every $A$-modules $L,M,N$. Can someone help me please ? Thank you
2026-05-03 12:01:48.1777809708
If $A$ is a semisimple algebra, then every $A$-module short exact sequence splits
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