Relative global dimensions and stable homotopy categories
Li Liang, Junpeng Wang
TL;DR
This paper investigates the finiteness of global Gorenstein AC-homological dimensions for rings and demonstrates that certain Gorenstein rings possess stable homotopy categories, advancing understanding in homological algebra.
Contribution
It provides new results on the finiteness conditions of Gorenstein AC-homological dimensions and establishes the existence of stable homotopy categories for specific Gorenstein rings.
Findings
Finiteness of global Gorenstein AC-homological dimensions studied
Left Gorenstein rings have stable homotopy categories
Improves previous results by Beligiannis
Abstract
In this paper we study the finiteness of global Gorenstein AC-homological dimensions for rings, and answer the questions posed by Becerril, Mendoza, P\'{e}rez and Santiago. As an application, we show that any left (or right) coherent and left Gorenstein ring has a projective and injective stable homotopy category, which improves the known result by Beligiannis.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra