Precisely, let $P$ be a projective module and $\partial:P\to Q$ be a module homomorphism. Then how do we prove that $Im\partial$ is still a projective module?
2026-03-27 12:03:07.1774612987
Is the Image of a projective module still a projective module?
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This is false. Every module is the image of a free (hence projective) module. Yet, non-projective modules exist.