Relative projective modules and relative injective modules

摘要

Let R be a ring, and n and d fixed non-negative integers. An R-module M is called (n, d)-injective if Ext(R)(d+1)(P, M ) = 0 for any n-presented R-module P . M is said to be (n, d)-projective if Ext(R)(1) (M, N ) = 0 for any (n, d)-injective R -module N . We use these concepts to characterize n -coherent rings and (n, d)-rings. Some known results are extended.