I was trying to prove the first statement using some characterizations of injective and projective modules but it did not work out. Could someone drop some hints?
2026-03-25 11:16:33.1774437393
If a left ideal I of R is an injective R-module then I is a projective R-module. Is the converse true?
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No: $\mathbb Z\subset \mathbb Z$ is a projective ideal which is not injective (because it is not divisible).