2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65055Let $(R,\fm)$ 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.10 pagesCommutative Algebra13C14; 13D45; 13H10text