2019/12/13 by Lars Winther Christensen, Sergio Estrada, Christensen, Lars Winther +9 · 2 citations
Mathematics · Physics and Astronomy · #16E05 #16E10 #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.1912.06575
openalex publication_date 2019/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a refinement of the Gorenstein flat dimension for complexes over an associative ring--the Gorenstein flat-cotorsion dimension--and prove that it, unlike the Gorenstein flat dimension, behaves as one expects of a homological dimension without extra assumptions on the ring. Crucially, we show that it coincides with the Gorenstein flat dimension for complexes where the latter is finite, and for complexes over right coherent rings--the setting where the Gorenstein flat dimension is known to behave as expected.