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 = infinity. v(R)(M) is defined as sup{n : M is n-FP-projective} and v(R) (M) = -1 if Ext(1) (M, N) not equal 0 for some FP-injective right R-module N. The right v-diniension r.v-dim(R) of R is defined to be the least nonnegative integer n such that v(R)(M) : n implies v(R)(M) = infinity for any right R-module M. If no such n exists, set r.v-dim(R) = infinity. The aim of this paper is to investigate n-FP-projective modules and the v-dimension of rings.
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