$(\mathcal{F},\mathcal{A})$-Gorenstein flat homological dimensions

Abstract

In this paper we develop the homological properties of the (L, A)-Gorenstein flat R-modules GF (F (R),A) proposed by Gillespie. Where the class A ⊆ Mod(R op ) sometimes corresponds to a duality pair (L, A). We study the weak global and finitistic dimensions that comes with GF (F (R),A) and show that over a (L, A)-Gorenstein ring, the functor − ⊗ R − is left balanced over Mod(R op ) × Mod(R) by the classes GF (F (R op ),A) × GF (F (R),A) . When the duality pair is (F (R), F PInj(R op )) we recover the G. Yang's result over a Ding-Chen ring, and we see that is new for (Lev(R), AC(R op )) among others.