Homological dimensions and regular rings
Alina Iacob, Srikanth B. Iyengar
TL;DR
This paper proves that for noetherian rings, the injective dimension of complexes aligns with certain homological properties, and extends similar results to flat and projective dimensions, advancing understanding of homological dimensions in algebra.
Contribution
It establishes the affirmative answer to a question by Avramov and Foxby for noetherian rings and connects the problem to the homotopy category of complexes of injective modules.
Findings
Injective dimension of complexes equals the homological dimension for noetherian rings
Results extended to flat and projective dimensions
Uses homotopy category of complexes of injective modules
Abstract
A question of Avramov and Foxby concerning injective dimension of complexes is settled in the affirmative for the class of noetherian rings. A key step in the proof is to recast the problem on hand into one about the homotopy category of complexes of injective modules. Analogous results for flat dimension and projective dimension are also established.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Rings, Modules, and Algebras