- Current Issue - Ahead of Print Articles - All Issues - Search - Open Access - Information for Authors - Downloads - Guideline - Regulations ㆍPaper Submission ㆍPaper Reviewing ㆍPublication and Distribution - Code of Ethics - For Authors ㆍOnline Submission ㆍMy Manuscript - For Reviewers - For Editors
 When is $C(X)$ an EM-ring? Commun. Korean Math. Soc. 2022 Vol. 37, No. 1, 17-29 https://doi.org/10.4134/CKMS.c200456Published online July 7, 2021Printed January 31, 2022 Emad Abuosba, Isaaf Atassi The University of Jordan; The University of Jordan Abstract : A commutative ring with unity $R$ is called an EM-ring if for any finitely generated ideal $I$ there exist $a$ in $R$ and a finitely generated ideal $J$ with $\limfunc{Ann}(J)=0$ and $I=aJ$. In this article it is proved that $C(X)$ is an EM-ring if and only if for each $U\in Coz\left( X\right)$, and each $g\in C^{\ast }\left( U\right)$ there is $V\in Coz\left( X\right)$ such that $U\subseteq V$, $\overline{V}=X$, and $g$ is continuously extendable on $V$. Such a space is called an EM-space. It is shown that EM-spaces include a large class of spaces as F-spaces and cozero complemented spaces.\ It is proved among other results that $X$ is an EM-space if and only if the Stone-\v{C}ech compactification of $X$ is. Keywords : $C(X)$, EM-ring, generalized morphic ring, PP-ring, PF-ring, basically disconnected space, F-space, cozero complemented space MSC numbers : 13A15, 54C30, 54C45 Supported by : This article is a part of the Ph.D. thesis prepared by the second author under supervision of the first in The University of Jordan. Downloads: Full-text PDF   Full-text HTML

 Copyright © Korean Mathematical Society. (Rm.1109) The first building, 22, Teheran-ro 7-gil, Gangnam-gu, Seoul 06130, Korea Tel: 82-2-565-0361  | Fax: 82-2-565-0364  | E-mail: paper@kms.or.kr   | Powered by INFOrang Co., Ltd