SV-rings are commutative rings whose factor rings modulo prime ideals are valuation rings. SV-rings occur most naturally in connection with partially ordered rings (= porings) and have been studied only in this context so far. The present note first develops the theory of SV-rings systematically, without assuming the presence of a partial order. Particular attention is paid to the question of a...

Contents 1. Introduction 2. Real closed rings-a model theoretic tour 3. Computation of the z-radical in C(X) 4. A sentence in the language of rings separating continuous semi-algebraic from arbitrary continuous functions 5. Super real closed rings: Definition and basic properties 6. Υ-ideals 7. Localization of super real closed rings 8. Application: o-minimal structures on super real closed fie...

A von Neumann regular extension of a semiprime ring naturally deenes a epimorphic extension in the category of rings. These are studied, and four natural examples are considered, two in commutative ring theory, and two in rings of continuous functions.

let $l$ be a completely regular frame and $mathcal{r}l$ be the ringof continuous real-valued functions on $l$. we study the frame$mathfrak{o}(min(mathcal{r}l))$ of minimal prime ideals of$mathcal{r}l$ in relation to $beta l$. for $iinbeta l$, denoteby $textit{textbf{o}}^i$ the ideal${alphainmathcal{r}lmidcozalphain i}$ of $mathcal{r}l$. weshow that sending $i$ to the set of minimal prime ideals...