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单词 DiscreteValuationRing
释义

discrete valuation ring


A discrete valuation ring R is a principal ideal domainMathworldPlanetmath with exactly one nonzero maximal idealMathworldPlanetmath M. Any generator t of M is called a uniformizer or uniformizing element of R; in other words, a uniformizer of R is an element tR such that tM but tM2.

Given a discrete valuation ring R and a uniformizer tR, every element zR can be written uniquely in the form utn for some unit uR and some nonnegative integer n. The integer n is called the order of z, and its value is independent of the choice of uniformizing element tR.

Titlediscrete valuation ring
Canonical nameDiscreteValuationRing
Date of creation2013-03-22 12:16:40
Last modified on2013-03-22 12:16:40
Ownerdjao (24)
Last modified bydjao (24)
Numerical id9
Authordjao (24)
Entry typeDefinition
Classificationmsc 13F30
Classificationmsc 13H10
SynonymDVR
Related topicLocalRing
Related topicDiscreteValuation
Related topicValuationMathworldPlanetmath
Definesuniformizer
Definesuniformizing element
Definesorder
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更新时间:2025/5/4 8:00:11