Cohen--Macaulayness of tensor products

2002/09/24 by Leila Khatami, Siamak Yassemi, Khatami, Leila +1
Mathematics · #13C14 #13D45 #13H10 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #math.AC #msc:13C14 #msc:13D45 #msc:13H10

paper · pdf · doi:10.48550/arxiv.math/0209318

10 pages

arxiv created 2002/09/24 · openalex publication_date 2002/09/24 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Related

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• Special homological dimensions and Intersection Theorem
• On the depth of tensor products over Cohen-Macaulay rings
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