For questions related to projective modules, their structures, and properties.

We call a module $P$ over a ring $R$ *projective* if for every surjective $R$-module homomorphism $f : N \to M$, and every module homomorphism $g : P \to M$, there is a lift $h$. That is, there is a module homomorphism $h : P \to N$ with $fh = g$.

Alternatively, a module $P$ is projective if every short exact sequence $$0 \to A \to B \to P \to 0$$

of $R$-modules splits.

Projective modules can be viewed as generalizations of free modules, and every free module is projective.

Source: Projective module.