Friday, 2 October 2009

ac.commutative algebra - Tensor product is to flat as Hom is to ?

It might also be helpful to know that projective is equivalent to being a summand of a free module (apply Hom(M,text) to a presentation of M), and hence projectives are flat.
The converse is not true in general (e.g. mathbbQ is flat as a mathbbZ-module, but not projective), but for finitely presented modules over commutative rings, flat and projective are equivalent.

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