Bulletin of the
Korean Mathematical Society
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Bull. Korean Math. Soc.

Published online March 10, 2022

Copyright © The Korean Mathematical Society.

A generalization of w-linked extensions

Xiaoying Wu

Sichuan Normal University

Abstract

In this paper, the concepts of w-linked homomorphisms, the wφ-operation, and DWφrings are introduced. Also the relationships between wφ-ideals and w-ideals over a w-linked homomorphism φ : R → T are discussed.More precisely, it is shown that every wφ-ideal of T is a w-ideal of T. Besides,it is shown that if T is not a DWφring, then T must have an infinite number of maximal wφ-ideals. Finally we give an application of Cohen’s Theorem over w-factor rings, namely it is shown that an integral domain R is an SM-domain with w-dim(R) ≤ 1, if and only if for any nonzero w-ideal I of R, (R/I)w is an Artinian ring, if and only if for any nonzero element a ∈ R, (R/(a))w is
an Artinian ring, if and only if for any nonzero element a ∈ R, R satisfies the descending chain condition on w-ideals of R containing a.

Keywords: w-linked homomorphism; wφ-operation; DWφ ring; w-factor ring.

MSC numbers: 13B02,13E05

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