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Let m and n be fixed positive integers and M a right R- module. Recall that M is said to be (m, n)-injective if Ext1(P,M) = 0 for any (m, n)-presented right R-module P; M is said to be (m, n)-flat if Tor1(N, P) = 0 for any (m, n)-presented left R-module P. In terms of some derived functors, relative injective or relative flat resolutions and dimensions are investigated. As applications, some new characterizations of von Neumann regular rings and p.p. rings are given. © 2013 The Korean Mathematical Society.

RESOLUTIONS AND DIMENSIONS OF RELATIVE INJECTIVE MODULES AND RELATIVE FLAT MODULES