MODULES SATISFYING CERTAIN CHAIN CONDITIONS AND THEIR ENDOMORPHISMS

Title & Authors
MODULES SATISFYING CERTAIN CHAIN CONDITIONS AND THEIR ENDOMORPHISMS
Wang, Fanggui; Kim, Hwankoo;

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, $\small{End_RM}$ is a division ring.
Keywords
GV-torsion-free;w-module;w-Noetherian module;w-simple module;w-Artinian module;
Language
English
Cited by
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