Let $\iota:B \to A$ a ring homomorphism. If there is a map $\pi:A \to B$, s.t. $\pi(\iota(b)a) = b\pi(a)$ for all $a \in A$, $b \in B$, then $A$ is projective as a left $B$-module. Is the converse true?
2026-03-26 12:52:13.1774529533
If restricted module is projective, does left inverse exist?
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