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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)
  • Received : 2009.09.09
  • Accepted : 2010.07.27
  • Published : 2011.01.01

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

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