J. Korean Math. Soc. 2011; 48(1): 207-222
Printed January 1, 2011
https://doi.org/10.4134/JKMS.2011.48.1.207
Copyright © The Korean Mathematical Society.
Huayu Yin, Fanggui Wang, Xiaosheng Zhu, and Youhua Chen
Nanjing University, Sichuan Normal University, Nanjing University, Sichuan Normal University
Let $R$ be a commutative ring and let $M$ be a $GV$-torsionfree $R$-module. Then $M$ is said to be a $w$-module if ${\rm Ext}_R^1(R/J, M)=0$ for any $J\in GV(R)$, and the $w$-envelope of $M$ is defined by $M_w=\{x\in E(M) | Jx\subseteq M \mbox{ for some } J\in GV(R)\}$. In this paper, $w$-modules over commutative rings are considered, and the theory of $w$-operations is developed for arbitrary commutative rings. As applications, we give some characterizations of $w$-Noetherian rings and Krull rings.
Keywords: $GV$-ideal, $GV$-torsionfree module, $w$-module, $w$-Noetherian ring, Krull ring
MSC numbers: Primary 13A15, 13D99; Secondary 13E99, 13F05
2013; 50(5): 1051-1066
2022; 59(4): 821-841
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd