Let $F$ a field and $V$ an $F$-module (i.e. an $F$-vector space). Then $V$ has a basis, and so $V$ is free. All free modules are projective, so $V$ is projective too.
Is this ok?
2026-03-30 07:38:43.1774856323
Is this a valid proof for why all modules over a field are projective?
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