We have been given R, a semi-simple ring. My notes state without any justification that every R-module M is a quotient of a direct sum of copies of R. I guess this is supposed to be obvious but I can't see why this is. Thanks for any help figuring out the intermediate steps!
2026-04-11 19:29:00.1775935740
Simple question about R-modules
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I think the answer to my question is as follows: (1) M is generated by itself. (2) A subset S of M generates M if and only if the homomorphism from the direct sum of R over S to M is surjective. (3) Combining (1) and (2) gives the result.
Please feel free to tell me whether this is wrong. I am new to the theory of modules and not very confident in my understanding.