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http://dx.doi.org/10.4134/JKMS.2011.48.1.207

ω-MODULES OVER COMMUTATIVE RINGS  

Yin, Huayu (DEPARTMENT OF MATHEMATICS NANJING UNIVERSITY)
Wang, Fanggui (COLLEGE OF MATHEMATICS AND SOFTWARE SCIENCE SICHUAN NORMAL UNIVERSITY)
Zhu, Xiaosheng (DEPARTMENT OF MATHEMATICS NANJING UNIVERSITY)
Chen, Youhua (COLLEGE OF MATHEMATICS AND SOFTWARE SCIENCE SICHUAN NORMAL UNIVERSITY)
Publication Information
Journal of the Korean Mathematical Society / v.48, no.1, 2011 , pp. 207-222 More about this Journal
Abstract
Let R be a commutative ring and let M be a GV -torsionfree R-module. Then M is said to be a $\omega$-module if $Ext_R^1$(R/J, M) = 0 for any J $\in$ GV (R), and the w-envelope of M is defined by $M_{\omega}$ = {x $\in$ E(M) | Jx $\subseteq$ M for some J $\in$ GV (R)}. In this paper, $\omega$-modules over commutative rings are considered, and the theory of $\omega$-operations is developed for arbitrary commutative rings. As applications, we give some characterizations of $\omega$-Noetherian rings and Krull rings.
Keywords
GV-ideal; GV-torsionfree module; w-module; $\omega$-Noetherian ring; Krull ring;
Citations & Related Records

Times Cited By Web Of Science : 3  (Related Records In Web of Science)
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