FP-gr-projective Dimension And FP-gr-projective Module

This paper defines the FP-gr-projective dimension, and then gives the con-cept of FP-gr-projective modules. Moreover, their properties are studied. FP-gr-projective is a new concept in the category of graded modules following the concept of FP-projective in the usual module category. Through discussing the relationship between FP-gr-projective modules and FP-gr-injective modules in gr-coherent rings, we obtain some results on the existence of FP-gr-projective precovers、FP-gr-injective preenvelopes and their characterizations. In addi-tion, the paper also studies properties of some graded modules under graded ring extensions.