oaioai:CiteSeerX.psu:10.1.1.46.5951

Valuations and Dedekind's Prague Theorem

Abstract

To any field K we associate an entailment relation in the sense of Scott [12]. In this way we can interpret an abstract propositional theory representing a generic valuation ring of a field, and obtain a simple effective proof of Dedekind's Prague theorem [5,6]. Keywords: Valuations, Entailment relations. AMS class.: 13A10, 13B25, 54H99 1 Introduction To any field K we associate a relation ` between finite sets of non zero elements of K which satisfy the three conditions of an entailment relation in the sense of Scott [12], and some further simple conditions. In this way, we can give constructive sense of a generic valuation ring of a field. Alternatively, this can be seen as a generalisation of the notion of integral element, and this notion can be used to prove that a given element is integral. As an example, we present a simple effective proof of Dedekind's Prague theorem. 2 Valuations Let K be a field, that is a commutative ring in which any element is 0 or is invertible. We write..

Similar works

Full text

thumbnail-image
oaioai:CiteSeerX.psu:10.1.1.46.5951Last time updated on 10/22/2014

This paper was published in CiteSeerX.

Having an issue?

Is data on this page outdated, violates copyrights or anything else? Report the problem now and we will take corresponding actions after reviewing your request.