Maximal Cohen–Macaulay tensor products and vanishing of Ext modules
Kaito Kimura, Yuya Otake, Ryo Takahashi
Abstract
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.
Topics & Concepts
MathematicsConjectureTensor productPure mathematicsTensor (intrinsic definition)Property (philosophy)Algebra over a fieldPhilosophyEpistemologyCommutative Algebra and Its ApplicationsAlgebraic structures and combinatorial modelsRings, Modules, and Algebras