One-sided Gorenstein rings
Lars Winther Christensen, Sergio Estrada, Li Liang, Peder Thompson,, and Junpeng Wang
TL;DR
This paper explores properties of one-sided Gorenstein rings, extending known symmetric characteristics of Iwanaga--Gorenstein rings to a broader, non-noetherian context, and establishing new relations among homological invariants.
Contribution
It demonstrates that key Gorenstein properties and relations among homological invariants hold in one-sided, non-noetherian rings, broadening the understanding of Gorenstein homological algebra.
Findings
Gorenstein global dimensions relate similarly in one-sided rings
New relations among projective, injective, and finitistic dimensions
Results apply without the noetherian assumption
Abstract
Distinctive characteristics of Iwanaga--Gorenstein rings are typically understood through their intrinsic symmetry. We show that several of those that pertain to the Gorenstein global dimensions carry over to the one-sided situation, even without the noetherian hypothesis. Our results yield new relations among homological invariants related to the Gorenstein property, not only Gorenstein global dimensions but also the suprema of projective/injective dimensions of injective/projective modules and finitistic dimensions.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Commutative Algebra and Its Applications