Modules satisfying certain chain conditions and their endomorphisms
Bull. Korean Math. Soc. 2015 Vol. 52, No. 2, 549-556
Published online March 31, 2015
Fanggui Wang and Hwankoo Kim
Sichuan Normal University, Hoseo University
Abstract : 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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