Bull. Korean Math. Soc. 2013; 50(1): 11-24
Printed January 31, 2013
https://doi.org/10.4134/BKMS.2013.50.1.11
Copyright © The Korean Mathematical Society.
Yuedi Zeng and Jianlong Chen
Putian College, Southeast University
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
MSC numbers: 16D50, 16E50, 16E10
2015; 52(1): 125-135
2013; 50(2): 459-467
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