ω-MODULES OVER COMMUTATIVE RINGS

Title & Authors
ω-MODULES OVER COMMUTATIVE RINGS
Yin, Huayu; Wang, Fanggui; Zhu, Xiaosheng; Chen, Youhua;

Abstract
Let R be a commutative ring and let M be a GV -torsionfree R-module. Then M is said to be a $\small{\omega}$-module if $\small{Ext_R^1}$(R/J, M) = 0 for any J $\small{\in}$ GV (R), and the w-envelope of M is defined by $\small{M_{\omega}}$ = {x $\small{\in}$ E(M) | Jx $\small{\subseteq}$ M for some J $\small{\in}$ GV (R)}. In this paper, $\small{\omega}$-modules over commutative rings are considered, and the theory of $\small{\omega}$-operations is developed for arbitrary commutative rings. As applications, we give some characterizations of $\small{\omega}$-Noetherian rings and Krull rings.
Keywords
GV-ideal;GV-torsionfree module;w-module;$\small{\omega}$-Noetherian ring;Krull ring;
Language
English
Cited by
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