Relative FP-Projective Modules

Abstract

ABSTRACT 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 = ∞. ν R ( M ) is defined as sup{ n : M is n - FP -projective} and ν R ( M ) = − 1 if Ext 1 ( M , N ) ≠ 0 for some FP -injective right R -module N . The right ν-dimension r .ν-dim( R ) of R is defined to be the least nonnegative integer n such that ν R ( M ) ≥ n implies ν R ( M ) = ∞ for any right R -module M . If no such n exists, set r .ν-dim( R ) = ∞. The aim of this paper is to investigate n - FP -projective modules and the ν-dimension of rings. #Communicated by A. Facchini.