2018/02/14 by Wang, Zhanping, Yang, Gang · 1 citation
#13D05 #16E30 #18G35 #55U15 #FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.1802.05197
Let X be a class of left R-modules, Y be a class of right R-modules. In this paper, we introduce and study Gorenstein (X, Y)-flat modules as a common generalization of some known modules such as Gorenstein flat modules \citeEJT93, Gorenstein n-flat modules \citeSUU14, Gorenstein B-flat modules \citeEIP17, Gorenstein AC-flat modules \citeBEI17, Ω-Gorenstein flat modules \citeEJ00 and so on. We show that the class of all Gorenstein (X, Y)-flat modules have a strong stability. In particular, when (X, Y) is a perfect (symmetric) duality pair, we give some functorial descriptions of Gorenstein (X, Y)-flat dimension, and construct a hereditary abelian model structure on R-Mod whose cofibrant objects are exactly the Gorenstein (X, Y)-flat modules. These results unify the corresponding results of the aforementioned modules.