Topology Proceedings 45 (2015) pp. 301-313: Characterizing C(X) among intermediate C-rings on X

Topology Proceedings 43 (2014) pp. 69-82: C and C* among intermediate rings

Given a completely regular Hausdorff space X, an intermediate ring A(X) is a ring of real valued continuous functions between C∗(X) and C(X). We discuss two correspondences between ideals in A(X) and z-filters on X, both reviewing old results and introducing new results. One correspondence, ZA, extends the well-known correspondence between ideals in C∗(X) and zfilters on X. The other, ZA, exten...

Mappings to Realcompactifications

In this paper, we introduce and study  a mapping from the collection of all  intermediate rings of $C(X)$ to the collection of all  realcompactifications of $X$ contained in $beta X$. By establishing the relations between this mapping and its converse,  we give a different approach to the main statements of De et. al. Using these, we provide different answers to the   four basic questions...

On constant products of elements in skew polynomial rings

Let $R$ be a reversible ring which is $alpha$-compatible for an endomorphism $alpha$ of $R$ and $f(X)=a_0+a_1X+cdots+a_nX^n$ be a nonzero skew polynomial in $R[X;alpha]$. It is proved that if there exists a nonzero skew polynomial $g(X)=b_0+b_1X+cdots+b_mX^m$ in $R[X;alpha]$ such that $g(X)f(X)=c$ is a constant in $R$, then $b_0a_0=c$ and there exist nonzero elements $a$ and $r$ in $R$ such tha...

Topology Proceedings 8 (1983) pp. 285-301: DENSE HOMEOMORPHIC SUBSPACES OF X^* AND OF (EX)^*

z-Ideals and zº-Ideals in the Factor Rings of C(X)