Gorenstein FP_n-injective(Flat)Complexes

In this paper,firstly,we give the notion of Gorenstein FP_n-injective(flat)mod-ules and Gorenstein FP_n-injective(flat)complexes and investigate the homological properties of them.We give some equivalent characterizations of Gorenstein FP_n-injective modules in(n-1)-coherent ring.Secondly,we introduce Gorenstein FP_n objects in the complex category,and investigate the relationship of homological prop-erties between Gorenstein FP_n-injective(flat)complex and each terms.Finally,we generalize the notion of FP-Gorenstein cotorsion module to complex category and prove that every complex has a FP-Gorenstein cotorsion preenvelop over coherent rings.