Article

Remarks on intermediate C-rings of C(X)

Published in: Quaestiones Mathematicae
Volume 41 , issue 5 , 2018 , pages: 675–682

DOI: 10.2989/16073606.2017.1401015

Author(s): Mehdi Parsinia Departemant of Mathematics, Iran

Keywords: 54C30 , 46E25 , 54C30 , 46E25

Abstract

Let X be a Tychonoﬀ space and A(X) be a subring of C(X) containing C^∗(X). We introduce the notion of -ideal in A(X). It is observed that the class of -ideals contains the class of z_A-ideals and is contained in the class of z-ideals of A(X). These containments may be proper. It turns out that coincidence of z-ideals of A(X) with -ideals characterizes intermediate C-rings of C(X).

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