On (strongly) Gorenstein (semi)hereditary rings
Najib Mahdou, Mohammed Tamekkante
TL;DR
This paper introduces and explores Gorenstein (semi)hereditary rings, focusing on those with Gorenstein homological dimensions at most 1, including special cases termed strongly Gorenstein (semi)hereditary rings.
Contribution
It defines and studies a new class of rings characterized by Gorenstein homological dimensions, expanding the understanding of their structure and properties.
Findings
Introduction of Gorenstein (semi)hereditary rings with dimension ≤ 1
Identification of strongly Gorenstein (semi)hereditary rings as special cases
Analysis of properties and implications of these rings
Abstract
In this paper, we introduce and study the rings of Gorenstein homological dimensions small or equal than 1, which we call Gorenstein (semi)hereditary rings, specially particular cases of these rings, which we call strongly Gorenstein (semi)hereditary rings.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Nonlinear Waves and Solitons · Advanced Topics in Algebra