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Mar 4 at 8:31 comment added Claudius Theorem 7.19 in Lam's book actually only talks about a finite-dimensional $k$-algebra $R$ as becomes clear from the preceding paragraph. I think that, at the very least, you need that $R$ is Artin, because otherwise $R/\mathrm{rad}(R)$ may not be semisimple.
Sep 11, 2018 at 8:23 vote accept Longma
Sep 11, 2018 at 8:23 comment added Longma Thanks a lot! I was out of Internet for ten days, sorry.
Aug 30, 2018 at 17:21 history answered Alex Dugas CC BY-SA 4.0