Strongly Gorenstein flat and Gorenstein FP-injective modules

In this paper, we first study the properties of strongly Gorenstein flat (resp. Gorenstein FP-injective) modules which are special Gorenstein projective (resp. Gorenstein injective) modules, and use them to prove that the global strongly Gorenstein flat dimension and the global Gorenstein FP-injective dimension of a ring R are identical when R is n-FC or commutative coherent. Finally, we show that if R is a commutative Noetherian ring, then, for any R-module M, SGfdRM = GpdRM, and hence SGfdRM ∞ if and only if GfdRM ∞, where SGfdRM denotes the strongly Gorenstein flat dimension of M.