A note on Cohen-Macaulay descent
Mohsen Asgharzadeh
TL;DR
This paper explores how Cohen-Macaulay properties behave under tensor products with perfect modules, focusing on Cohen-Macaulay and perfect defects, and relates these to associated prime ideals.
Contribution
It introduces new insights into Cohen-Macaulay and perfect defects under tensor products and links these properties to associated prime ideals.
Findings
Cohen-Macaulay defect behavior under tensor products analyzed
Introduction of perfect defect concept for modules
Connection established between tensor products and associated primes
Abstract
We investigate the behavior of Cohen-Macaulay defect undertaking tensor product with a perfect module. Consequently, we study the perfect defect of a module. As an application, we connect to associated prime ideals of tensor products.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Algebraic structures and combinatorial models · Algebraic Geometry and Number Theory