## Mehdi Parsinia

*On the mappings ${\mathcal Z}_A$ and $\Im_A$ in intermediate rings of $C(X)$*

Comment.Math.Univ.Carolin. 59,3 (2018) 383-390.**Abstract:**In this article, we investigate new topological descriptions for two well-known mappings ${\mathcal Z}_A$ and $\Im_A$ defined on intermediate rings $A(X)$ of $C(X)$. Using this, coincidence of each two classes of $z$-ideals, ${\mathcal Z}_A$-ideals and $\Im_A$-ideals of $A(X)$ is studied. Moreover, we answer five questions concerning the mapping $\Im_A$ raised in [J.~Sack, S.~Watson, {\it $C$ and $C^*$ among intermediate rings}, Topology Proc.\ {\bf 43} (2014), 69--82].

**Keywords:** $z$-ideal; ${\mathcal Z}_A$-ideal; $\Im_A$-ideal; $z$-filter; ${\mathcal Z}_A$-filter; $\Im_A$-filter; intermediate ring

**DOI:** DOI 10.14712/1213-7243.2015.249

**AMS Subject Classification:** 54C30 46E25

PDF