A study on Cartan-Eilenberg Gorenstein n-FP-injective and n-flat complexes

Abstract

This article introduces and studies the concept of Cartan-Eilenberg (CE) Gorenstein n-FP-injective and Cartan-Eilenberg Gorenstein n-flat complexes. We prove that every CE-n-FP-injective complex is CE-injective if and only if R is a left Noetherian ring. In addition, we show that every CE-n-FP-injective complex of R-modules is CE-Gorenstein n-FP-injective over a Noetherian ring. Finally, we give the relation between the CE-Gorenstein n-FP-injective complex and the CE-Gorenstein n-flat complex.