Endofunctors of singularity categories characterizing Gorenstein rings
Takuma Aihara, Ryo Takahashi
TL;DR
This paper demonstrates that specific contravariant endofunctors of singularity categories can be used to characterize Gorenstein rings, providing a new categorical perspective on their properties.
Contribution
It introduces a novel approach using endofunctors of singularity categories to identify Gorenstein rings, advancing the understanding of their categorical and algebraic structure.
Findings
Contravariant endofunctors characterize Gorenstein rings
New categorical tools for ring classification
Enhanced understanding of singularity categories
Abstract
In this paper, we prove that certain contravariant endofunctors of singularity categories characterize Gorenstein rings.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Commutative Algebra and Its Applications · Advanced Topics in Algebra