Theorem

Characterizations of semisimplicity

0) $R_R$ is a direct sum of simple submodules; 1) Every right $R$ module is a sum of simple submodules; 2) Every right $R$ module is projective; 3) Every right $R$ module is injective; 4) $R$ has right global dimension $0$; 5) all the left-handed versions of previous conditions.

Reference(s)

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