Maximal Cohen-Macaulay tensor products and vanishing of Ext modules. (English) Zbl 1520.13016
Summary: In this paper, we investigate the maximal Cohen-Macaulay property of tensor products of modules, and then give criteria for projectivity of modules in terms of vanishing of Ext modules. One of the applications shows that the Auslander-Reiten conjecture holds for Cohen-Macaulay normal rings.
{© 2022 The Authors. The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence.}
{© 2022 The Authors. The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence.}
MSC:
| 13C14 | Cohen-Macaulay modules |
| 13D07 | Homological functors on modules of commutative rings (Tor, Ext, etc.) |
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