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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 .
Defines:
uniformizer, uniformizing element, order
Related:
LocalRing, DiscreteValuation, Valuation
Synonym:
DVR
Type of Math Object:
Definition
Major Section:
Reference
Mathematics Subject Classification
13F30 Valuation rings13H10 Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.)
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May 21
new question: pure subgroups by lvoyster
new correction: Typo in M\"obius function? by Aleph Zero
new collection: analytic number theory by Aleph Zero
May 20
new question: Taylor's Series Query! by unlord
new question: Laplace transform by J
new question: Residue Calculus by J
May 19
new Education: Project: PlanetMath Outlines Series by unlord


