FP-GR-INJECTIVE MODULES

In this paper, we give some characterizations of FP-grinjective R-modules and graded right R-modules of FP-gr-injective dimension at most n. We study the existence of FP-gr-injective envelopes and FP-gr-injective covers. We also prove that (1) (^⊥gr-FI, gr-FI) is a hereditary cotorsion theory if and only if R is a left gr-coherent ring, (2) If R is right gr-coherent with FP-gr-id(R_R) ≤ n, then (gr-FI_n, gr-F _n^⊥) is a perfect cotorsion theory, (3) (^⊥gr-FI_n, gr-FI_n) is a cotorsion theory, where gr-FI denotes the class of all FP-gr-injective left R-modules, gr-FI_n is the class of all graded right R-modules of FP-gr-injective dimension at most n. Some applications are given.