I need a hint about this question, I know all the different ways of defining a projective module, but, I don’t know where to start: R is an left Artinian ring, M is a left R-module. I need to prove M/J(R)M is a projective R/J(R) module. Could anyone please help me to prove it?
2026-02-22 19:27:22.1771788442
Projectivity of a module
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Since R/J is semisimple artinian, all short exact sequences of left R/J-modules split, so in particular all left R/J-modules are projective.