2025/08/08 by Asadollahi, Javad, Hafezi, Rasool, Sadeghi, Somayeh
#16E30 #16S85 #18E35 #55P60 #FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2508.06458
In this paper, we investigate a non-commutative version of strongly flat modules, which is based on the concept of universal localization introduced by Cohn. We consider a set σ consisting of maps of finitely generated projective R-modules, where R is not necessarily a commutative ring. Let Rσ denote the universal localization of R with respect to σ. The class of σ-strongly flat modules is defined as the left class in the cotorsion pair generated by Rσ. We examine the homotopy category of σ-strongly flat modules and demonstrate that the thick subcategory \mathscrSσ, consisting of acyclic complexes, wherein all syzygies are σ-strongly flat, forms a precovering class within this homotopy category. This implies that the quotient map from \mathbbK(σ-SF) to \mathbbK(σ-SF)/\mathscrSσ always has a fully faithful right adjoint.