# MODULES SATISFYING CERTAIN CHAIN CONDITIONS AND THEIR ENDOMORPHISMS

• Wang, Fanggui (College of Mathematics Sichuan Normal University) ;
• Kim, Hwankoo (School of Computer and Information Engineering Hoseo University)
• Received : 2014.03.07
• Published : 2015.03.31

#### 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, $End_RM$ is a division ring.

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