Maximal Cohen–Macaulay tensor products and vanishing of Ext modules
نویسندگان
چکیده
In this paper, we investigate the maximal Cohen-Macaulay property of tensor products modules, and then give criteria for projectivity modules in terms vanishing Ext modules. One applications shows that Auslander-Reiten conjecture holds normal rings.
منابع مشابه
Of Module Structures , Vanishing of Ext , and Extended Modules
Let (R, m) and (S, n) be commutative Noetherian local rings, and let φ : R→ S be a flat local homomorphism such that mS = n and the induced map on residue fields R/m→ S/n is an isomorphism. Given a finitely generated R-module M , we show that M has an S-module structure compatible with the given R-module structure if and only if Ext R (S,M) = 0 for each i ≥ 1. We say that an S-module N is exten...
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ژورنال
عنوان ژورنال: Bulletin of The London Mathematical Society
سال: 2022
ISSN: ['1469-2120', '0024-6093']
DOI: https://doi.org/10.1112/blms.12705