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.