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http://dx.doi.org/10.4134/CKMS.c200456

WHEN IS C(X) AN EM-RING?  

Abuosba, Emad (Department of Mathematics The University of Jordan)
Atassi, Isaaf (Department of Mathematics The University of Jordan)
Publication Information
Communications of the Korean Mathematical Society / v.37, no.1, 2022 , pp. 17-29 More about this Journal
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 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 ∈ Coz (X), and each g ∈ C* (U) there is V ∈ Coz (X) such that U ⊆ V, ${\bar{V}}=X$, 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-Čech compactification of X is.
Keywords
C(X); EM-ring; generalized morphic ring; PP-ring; PF-ring; basically disconnected space; F-space; cozero complemented space;
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Times Cited By KSCI : 1  (Citation Analysis)
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