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uniformizing parameter - Übersetzung nach russisch
PRINCIPAL IDEAL DOMAIN THAT IS A LOCAL RING AND NOT A FIELD
M-adic topology; Uniformizing parameter; Uniformizing element; Uniformizer; Uniformiser; Uniformizers; Uniformisers; Uniformising parameter; Uniformising element
uniformizing parameter
математика
униформизирующий параметр
m-adic topology
математика
m-адическая топология
discrete valuation ring
кольцо дискретного нормирования
Definition
head-first
also headfirst
If you move head-first in a particular direction, your head is the part of your body that is furthest forward as you are moving.
He had apparently fallen head-first down the stairwell...
ADV: ADV after v
Wikipedia
Discrete valuation ring
In abstract algebra, a discrete valuation ring (DVR) is a principal ideal domain (PID) with exactly one non-zero maximal ideal.
This means a DVR is an integral domain R which satisfies any one of the following equivalent conditions:
- R is a local principal ideal domain, and not a field.
- R is a valuation ring with a value group isomorphic to the integers under addition.
- R is a local Dedekind domain and not a field.
- R is a Noetherian local domain whose maximal ideal is principal, and not a field.
- R is an integrally closed Noetherian local ring with Krull dimension one.
- R is a principal ideal domain with a unique non-zero prime ideal.
- R is a principal ideal domain with a unique irreducible element (up to multiplication by units).
- R is a unique factorization domain with a unique irreducible element (up to multiplication by units).
- R is Noetherian, not a field, and every nonzero fractional ideal of R is irreducible in the sense that it cannot be written as a finite intersection of fractional ideals properly containing it.
- There is some discrete valuation ν on the field of fractions K of R such that R = {0} {x K : ν(x) ≥ 0}.
