discrete valuation ring
A discrete valuation ring is a principal ideal domain with exactly one nonzero maximal ideal . Any generator of is called a uniformizer or uniformizing element of ; in other words, a uniformizer of is an element such that but .
Given a discrete valuation ring and a uniformizer , every element can be written uniquely in the form for some unit and some nonnegative integer . The integer is called the order of , and its value is independent of the choice of uniformizing element .
Title | discrete valuation ring |
Canonical name | DiscreteValuationRing |
Date of creation | 2013-03-22 12:16:40 |
Last modified on | 2013-03-22 12:16:40 |
Owner | djao (24) |
Last modified by | djao (24) |
Numerical id | 9 |
Author | djao (24) |
Entry type | Definition |
Classification | msc 13F30 |
Classification | msc 13H10 |
Synonym | DVR |
Related topic | LocalRing |
Related topic | DiscreteValuation |
Related topic | Valuation |
Defines | uniformizer |
Defines | uniformizing element |
Defines | order |