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Let R be a ring, and n and d fixed non-negative integers. An R-module M is called n d -injective if Ext d+1 R P M = 0 for any n-presented R-module P. M is said to be n d -projective if Ext 1 R 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.doi:10.1080/00927870600649111 fatcat:scsbnof6z5afpbzvedsrjqfmna