Prove that free modules are projective.
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2026-03-29 19:26:31.1774812391
Prove that free modules are projective
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Definition: $M$ is projective iff for every surjective morphism $f:A\rightarrow B$, and every morphism $g:M\rightarrow B$ there is morphism $h:M\rightarrow A$ such that $fh=g$.
Now if $M$ is free with base $\{x_i\}$ then we can define $g$ setting $x_i\mapsto a_i\in f^{-1}(g(x_i))$.