SERRE’S CONDITION FOR TENSOR PRODUCTS AND N-TOR-RIGIDITY OF MODULES
نویسندگان
چکیده
We study Serre’s condition (Sn) for tensor products of modules over a commutative noetherian local ring R. Specifically, we consider the following question. For finitely generated R-modules M and N, either which is (n+1)-Tor-rigid, if product M⊗RN satisfies (Sn+1), then does ToriR(M,N)=0 hold all i≥1? The aim this paper to give an affirmative answer question assume freeness on modules. As applications, recover several known results.
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ژورنال
عنوان ژورنال: Journal of Commutative Algebra
سال: 2023
ISSN: ['1939-0807', '1939-2346']
DOI: https://doi.org/10.1216/jca.2023.15.55