Covers And Envelopes Of Modules With Finite Fp-gorenstein Cotorsion Dimensions

Let R be a ring, n a fixed nonnegative integer and Fnthe class of all left R-modules of F P-Gorenstein cotorsion dimensions at most n.First some properties of Fnare given, we prove that (F⊥n, Fn) is a perfectcotorsion theory over a left coherent ring R, then, all left R-modules over a leftcoherent R admit Fn-covers and Fn-preenvelopes.Second we investigate the Fn-dimensions of modules and rings in terms of leftFn-resolutions and right Fn-resolutions, Study some properties of Fn-dimensions.We given some equivalent characterizations of that right Fn-dim(M) at most m orFn-dim(R) at most m.