A NOTE ON w-NOETHERIAN RINGS

Title & Authors
A NOTE ON w-NOETHERIAN RINGS
Xing, Shiqi; Wang, Fanggui;

Abstract
Let R be a commutative ring. An R-module M is called a w-Noetherian module if every submodule of M is of w-finite type. R is called a w-Noetherian ring if R as an R-module is a w-Noetherian module. In this paper, we present an exact version of the Eakin-Nagata Theorem on w-Noetherian rings. To do this, we prove the Formanek Theorem for w-Noetherian rings. Further, we point out by an example that the condition ($\small{{\dag}}$) in the Chung-Ha-Kim version of the Eakin-Nagata Theorem on SM domains is essential.
Keywords
w-moudle;w-finite type;w-Noetherian module;w-Noetherianring;
Language
English
Cited by
1.
Overrings of Prüfer v-multiplication domains, Journal of Algebra and Its Applications, 2017, 16, 08, 1750147
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