Gorenstein flat and projective (pre)covers
Sergio Estrada, Alina Iacob, Sinem Odabasi
TL;DR
This paper investigates the properties of Gorenstein flat and projective complexes over right coherent rings, establishing their covering and precovering properties in the category of complexes of modules.
Contribution
It proves that Gorenstein flat complexes are covering over right coherent rings and Gorenstein projective complexes are special precovering when the ring is also left n-perfect.
Findings
Gorenstein flat complexes form a covering class in Ch(R)
Gorenstein projective complexes are special precovering under certain conditions
Results extend understanding of Gorenstein homological algebra in complex categories
Abstract
We consider a right coherent ring R. We prove that the class of Gorenstein flat complexes is covering in the category of complexes of left R-modules Ch(R). When R is also left n-perfect, we prove that the class of Gorenstein projective complexes is special precovering in Ch(R).
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Nonlinear Waves and Solitons · Commutative Algebra and Its Applications