When is C(X) an EM-ring?
Commun. Korean Math. Soc.
Published online July 7, 2021
Emad Abuosba and 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 exists a in R and a finitely generated ideal J with Ann(J)=0 and I=aJ. In this article we show that C(X) is an EM-ring if and only if for any cozero set U in X there exists a dense cozero set V such that U is contained in V and C*-embedded in it. We call such a space an EM-space. We found that EM-spaces include large classes of spaces as F-spaces and cozero complemented spaces. We proved among other results that X is an EM-space if and only if βX 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
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