On Gorenstein global dimension in trivial ring extensions
Najib Mahdou, Mohammed Tamekkante
TL;DR
This paper investigates how the Gorenstein homological dimension of a ring compares to that of its trivial ring extension by a module, providing insights into their relationship.
Contribution
It introduces a comparison framework for Gorenstein homological dimensions between a ring and its trivial extension, advancing understanding in Gorenstein homological algebra.
Findings
Established conditions under which the Gorenstein dimensions are equal
Derived bounds relating the dimensions of the ring and its extension
Provided examples illustrating the theoretical results
Abstract
In this paper, we compare the Gorenstein homological dimension of a ring and of its trivial ring extension by an module .
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Commutative Algebra and Its Applications