Let $E(V)$ be the exterior algebra of a vector space $V$ (I've also seen this denoted $\Lambda(V)$).Is it true that any projective $E(V)$-module is necessarily free? If it's any easier, is it at least true if we assume $V$ has finite dimension?
This popped into my head for some reason while I was experimenting with projective complexes. I couldn't tell either way, but I hope it's not embarrassingly simple. Thanks.