### Some epimorphic regular contexts.

Skip to main content (access key 's'),
Skip to navigation (access key 'n'),
Accessibility information (access key '0')

Back to Simple Search
# Advanced Search

This is a description of some different approaches which have been taken to the problem of generalizing the algebraic closure of a field. Work surveyed is by Enoch and Hochster (commutative algebra), Raphael (categories and rings of quotients), Borho (the polynomial approach), and Carson (logic). Later work and applications are given.

Let G(X) denote the smallest (von Neumann) regular ring of real-valued functions with domain X that contains C(X), the ring of continuous real-valued functions on a Tikhonov topological space (X,τ). We investigate when G(X) coincides with the ring $C(X,{\tau}_{\delta})$ of continuous real-valued functions on the space $(X,{\tau}_{\delta})$, where ${\tau}_{\delta}$ is the smallest Tikhonov topology on X for which $\tau \subseteq {\tau}_{\delta}$ and $C(X,{\tau}_{\delta})$ is von Neumann regular. The compact and metric spaces for which $G\left(X\right)=C(X,{\tau}_{\delta})$ are characterized. Necessary, and different sufficient, conditions...

**Page 1**