Comparing generalized Gorenstein properties in semi-standard graded rings
Sora Miyashita
TL;DR
This paper explores and compares various generalized Gorenstein properties in semi-standard graded rings, highlighting both similarities and unique phenomena not found in standard graded rings.
Contribution
It introduces a comparative analysis of Gorenstein properties in semi-standard graded rings, revealing distinctive behaviors absent in standard graded rings.
Findings
Identifies commonalities between standard and semi-standard graded rings.
Highlights unique phenomena in semi-standard graded rings.
Provides a framework for understanding Gorenstein properties in generalized settings.
Abstract
Semi-standard graded rings are a generalized notion of standard graded rings. In this paper, we compare generalized notions of the Gorenstein property in semi-standard graded rings. We discuss the commonalities between standard graded rings and semi-standard graded rings, as well as elucidate distinctive phenomena present in semi-standard graded rings that are absent in standard graded rings.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Commutative Algebra and Its Applications · Rings, Modules, and Algebras