I've found this exercise, number $3.11$ from Introduction to homological algebra.
Prove that $\operatorname{Hom}(P, R) \neq 0 $ if $P$ is a nonzero projective left $R$-module.
Any hint?
2026-03-27 12:08:27.1774613307
Hom($P$, $R$) $\neq 0 $ if $P$ is a nonzero projective left $R$-module (Rotman)
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Hint: $P\oplus P'=R^{(\Lambda)}$ (a free module) for some set $\Lambda$ and some module $P'$.