Let R be a ring and M a right R-module. M is called n-FP-projective if Ext 1 M N = 0 for any right R-module N of FP-injective dimension ≤n, where n is a nonnegative integer or n = . R M is defined as sup n M is n-FP-projective and R M = −1 if Ext 1 M N = 0 for some FP-injective right R-module N . The right -dimension r -dim R of R is defined to be the least nonnegative integer n such that R M ≥ n implies R M = for any right R-module M . If no such n exists, set r -dim R = . The aim of this

more »

... is to investigate n-FP-projective modules and the -dimension of rings. R M = sup n M is n-FP-projective} and R M = −1 if Ext 1 M N = 0 for some FP-injective right R-module N . The right -dimension r · -dim R of a ring R is defined to be the least nonnegative integer n such that R M ≥ n implies R M = for any right R-module M. If no such n exists, set r · -dim R = . The purpose of this paper is to investigate these new notions.