Gorenstein weak global dimension is symmetric
Lars Winther Christensen, Sergio Estrada, and Peder Thompson
TL;DR
This paper proves that the Gorenstein weak global dimension of associative rings is symmetric with respect to left and right modules, establishing a key invariant property similar to the classical weak global dimension.
Contribution
It confirms the conjecture that the Gorenstein weak global dimension is symmetric, extending the understanding of Gorenstein homological dimensions in ring theory.
Findings
Gorenstein weak global dimension is symmetric for associative rings
The symmetry property parallels that of the classical weak global dimension
Provides a foundational result for Gorenstein homological algebra
Abstract
We study the Gorenstein weak global dimension of associative rings and its relation to the Gorenstein global dimension. In particular, we prove the conjecture that the Gorenstein weak global dimension is a left-right symmetric invariant -- just like the (absolute) weak global dimension.
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