Gorenstein flat dimension of complexes
Alina Iacob
TL;DR
This paper introduces a new Gorenstein flat dimension for complexes over certain rings, explores Gorenstein cohomology, and establishes connections with Tate cohomology, advancing homological algebra theory.
Contribution
It defines Gorenstein flat dimension for complexes, introduces Gorenstein and Tate cohomology for complexes over Gorenstein rings, and links these concepts.
Findings
Defined Gorenstein flat dimension for unbounded complexes
Introduced Gorenstein cohomology for complexes over Gorenstein rings
Established connections between absolute, Gorenstein, and Tate cohomology
Abstract
We define a notion of Gorenstein flat dimension for unbounded complexes over left GF-closed rings. Over Gorenstein rings we introduce a notion of Gorenstein cohomology for complexes; we also define a generalized Tate cohomology for complexes over Gorenstein rings, and we show that there is a close connection between the absolute, the Gorenstein and the generalized Tate cohomology.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra