Strongly Gorenstein flat and Gorenstein FP-injective modules

Authors: CHUNHUA YANG

Abstract: 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, SGfd_RM=Gpd_RM, and hence SGfd_RM< \infty if and only if Gfd_RM<\infty, where SGfd_RM denotes the strongly Gorenstein flat dimension of M.

Keywords: Strongly Gorenstein flat modules, global strongly Gorenstein flat dimension, Gorenstein FP-injective modules, global Gorenstein FP-injective dimension

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