Valuation ring
id:
valuation-ring-162-697196
title:
Valuation ring
text:
In abstract algebra, a valuation ring is an integral domain D such that for every non-zero element x of its field of fractions F, at least one of x or x−1 belongs to D. Given a field F, if D is a subring of F such that either x or x−1 belongs to
D for every nonzero x in F, then D is said to be a valuation ring for the field F or a place of F. Since F in this case is indeed the field of fractions of D, a valuation ring for a field is a valuation ring. Another way to characterize the valuation rin
brand slug:
wiki
category slug:
encyclopedia
description:
Concept in algebra
original url:
https://en.wikipedia.org/wiki/Valuation_ring
date created:
2004-09-07T20:59:21Z
date modified:
2024-08-27T11:40:38Z
main entity:
{"identifier":"Q12013681","url":"https://www.wikidata.org/entity/Q12013681"}
image:
fields total:
13
integrity:
15