REPRESENTATION THEORY AND RELATED TOPICS SEMINAR

ABSTRACT:  We introduce a generalization of the Gorenstein flat modules - the Gorenstein B-flat modules, GF_B, where B is a fixed class of right R-modules. We give sufficient conditions on B for the class of Gorenstein B-flat modules being closed under extensions, and we show that, when this is the case, GF_B is a covering class. We also prove that when GF_B is closed under extensions, there is a unique abelian model structure on the category of left R-modules (for any associative ring with identity) whose cofibrant objects are the Gorenstein B-flat modules. We also introduce a generalization of the Gorenstein projective modules, the Gorenstein FP n-projective modules, GP_n. We prove that when n ≥ 2, this class is precovering over any ring R. This is based on joint work with D. Bravo, S. Estrada, and M. Perez.