# RESOLUTIONS AND DIMENSIONS OF RELATIVE INJECTIVE MODULES AND RELATIVE FLAT MODULES

Zeng, Yuedi;Chen, Jianlong

• Published : 2013.01.31
• 28 6

#### Abstract

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.

#### Keywords

(m, n)-coherent ring;(m, n)-injective module;(m, n)-flat module;(pre)cover;(pre)envelope

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#### Cited by

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