[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.2015.52.2.541

A NOTE ON w-NOETHERIAN RINGS

Xing, Shiqi (College of Mathematics and Software Science Sichuan Normal University)
Wang, Fanggui (College of Mathematics and Software Science Sichuan Normal University)

Publication Information

Bulletin of the Korean Mathematical Society / v.52, no.2, 2015 , pp. 541-548 More about this Journal

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 ( ${\dag}$ ) 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;

Citations & Related Records

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