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Cohen–Macaulayness of Tensor Product

By Leila Khatami and Siamak Yassemi


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 Tor R i (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

Year: 2008
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