The depth formula for modules with reducible complexity
Petter Andreas Bergh, David Jorgensen
TL;DR
This paper proves the depth formula for certain modules over Cohen-Macaulay local rings when one module has reducible complexity, extending understanding of module interactions in commutative algebra.
Contribution
It establishes the validity of the depth formula for modules with reducible complexity under specific conditions, a novel result in the study of module theory.
Findings
Depth formula holds for Tor-independent modules with reducible complexity.
Validates the depth formula in new cases over Cohen-Macaulay local rings.
Advances the understanding of module interactions in algebra.
Abstract
We prove that the depth formula holds for -independent modules in certain cases over a Cohen-Macaulay local ring, provided one of the modules has reducible complexity.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Algebraic structures and combinatorial models · Rings, Modules, and Algebras