Tensor products of Cohen-Macaulay rings: Solution to a problem of Grothendieck

DOI10.1016/S0021-8693(02)00019-4zbMath1087.13507arXivmath/0606692MaRDI QIDQ1849089

Salah-Eddine Kabbaj, Samir Bouchiba

Publication date: 28 November 2002

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0606692

zbMATH Keywords

tensor productsCohen-Macaulay property

Mathematics Subject Classification ID

Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) (13H10) Cohen-Macaulay modules (13C14)

Related Items (19)

ON CONJUGATE PRIME IDEALS OF TENSOR PRODUCTS OF k-ALGEBRAS ⋮ Local dimension theory of tensor products of algebras over a ring ⋮ The K\"ahler Different of a Set of Points in $\mathbb{P}^m\times\mathbb{P}^n$ ⋮ Chains of prime ideals in tensor products of algebras ⋮ Local cohomology of binomial edge ideals and their generic initial ideals ⋮ Tensor products of some special rings. ⋮ Commuting varieties of \(r\)-tuples over Lie algebras. ⋮ The essential skeleton of a product of degenerations ⋮ Embedding Dimension and Codimension of Tensor Products of Algebras over a Field ⋮ Cohen-Macaulay, Gorenstein, complete intersection and regular defect for the tensor product of algebras ⋮ Seidenberg's Inequalities for Tensor Products of Algebras ⋮ KRULL DIMENSION OF TENSOR PRODUCTS OF PULLBACKS ⋮ Sequentially Cohen-Macaulay Modules Under Base Change ⋮ AF-Domains and Their Generalizations ⋮ Reflexive hull discriminants and applications ⋮ Tensor Products of Approximately Cohen–Macaulay Rings ⋮ On Krull and Valuative Dimension of Tensor Products of Algebras ⋮ Regularity and related properties in tensor products of algebras over a field ⋮ On Krull dimension of tensor products of algebras arising from AF-domains

Cites Work

• The dimension of tensor products of \(k\)-algebras arising from pullbacks
• Éléments de géométrie algébrique. IV: Étude locale des schémas et des morphismes de schémas. (Séconde partie)
• On tensor products of Gorenstein rings
• The Dimension of the Tensor Product of Two Field Extensions
• The Krull Dimensions of Tensor Products of Commutative Algebras over a Field
• On the minimal prime ideals of a tensor product of two fields
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