Cohen--Macaulayness of tensor products

Details Cohen--Macaulayness of tensor products Cohen--Macaulayness of tensor products

2002-09-24

arxiv.org/abs/math/0209318v1

Mathematics

Commutative Algebra

10 pages

Scientific paper

Let $(R,\fm)$ 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.

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