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RESOLUTIONS AND DIMENSIONS OF RELATIVE INJECTIVE MODULES AND RELATIVE FLAT MODULES
Zeng, Yuedi,Chen, Jianlong Korean Mathematical Society 2013 대한수학회보 Vol.50 No.1
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 $Ext^1$(P, M) = 0 for any ($m$, $n$)-presented right R-module P; M is said to be ($m$, $n$)-flat if $Tor_1$(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.
Resolutions and dimensions of relative injective modules and relative flat modules
Yuedi Zeng,Jianlong Chen 대한수학회 2013 대한수학회보 Vol.50 No.1
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.