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|Paper IPM / M / 754||
Let (R,m) be a commutative Noetherian local ring. Suppose that M and N are finitely generated modules over R such that M has finite projective dimension and such that ToriR(M,N)=0 for all i > 0. The main result of this note gives a condition on M which is necessary and sufficient for the tensor product of M and N to be a Cohen-Macaulay module over R, provided N is itself a Cohen-Macaulay module.
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