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Bull. Korean Math. Soc. 2015; 52(2): 549-556

Printed March 31, 2015

https://doi.org/10.4134/BKMS.2015.52.2.549

Copyright © The Korean Mathematical Society.

Modules satisfying certain chain conditions and their endomorphisms

Fanggui Wang and Hwankoo Kim

Sichuan Normal University, Hoseo University

Abstract

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In this paper, we characterize $w$-Noetherian modules in terms of polynomial modules and $w$-Nagata modules. Then it is shown that for a finite type $w$-module $M$, every $w$-epimorphism of $M$ onto itself is an isomorphism. We also define and study the concepts of $w$-Artinian modules and $w$-simple modules. By using these concepts, it is shown that for a $w$-Artinian module $M$, every $w$-monomorphism of $M$ onto itself is an isomorphism and that for a $w$-simple module $M$, $\End_R M$ is a division ring.

Keywords: GV-torsion-free, $w$-module, $w$-Noetherian module, $w$-simple module, $w$-Artinian module

MSC numbers: 13A15, 13E05, 13E10

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