TL;DR
This paper explores the properties of Gorenstein flat dimension over arbitrary rings, extending known results beyond Noetherian rings, and examines its relationship with Gorenstein projective dimension.
Contribution
It generalizes the concept of Gorenstein flat dimension to all associative rings and analyzes its connection to Gorenstein projective dimension.
Findings
Gorenstein flat dimension refines classical flat dimension over any ring
Established relations between Gorenstein flat and Gorenstein projective dimensions
Extended results previously limited to Noetherian rings
Abstract
Unlike the Gorenstein projective and injective dimensions, the majority of results on the Gorenstein flat dimension have been established only over Noetherian (or coherent) rings. Naturally, one would like to generalize these results to any associative ring. In this direction, we show that the Gorenstein flat dimension is a refinement of the classical flat dimension over any ring; and we investigate the relations between the Gorenstein projective dimension and the Gorenstein flat dimension.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Nonlinear Waves and Solitons · Advanced Topics in Algebra