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What (who) is uniformizing parameter - definition
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
Discrete valuation ring
In abstract algebra, a discrete valuation ring (DVR) is a principal ideal domain (PID) with exactly one non-zero maximal ideal.
Parameter (computer programming)
IN COMPUTER PROGRAMMING, SPECIAL KIND OF VARIABLE THAT HOLDS DATA THAT WAS PASSED AS AN ARGUMENT TO A SUBROUTINE
Argument (computer science); Argument (programming); Parameter (programming); Formal parameter; Actual parameter; Parameters (computer science); Formal parameters; Function parameter; Argument (computing); Parameter (computer science); Parameter (computing); Output parameter; Out parameter; Return parameter; Argument (computer programming); Input parameter; Input value; Output value; Actual parameters
In computer programming, a parameter or a formal argument is a special kind of variable used in a subroutine to refer to one of the pieces of data provided as input to the subroutine. These pieces of data are the values of the arguments (often called actual arguments or actual parameters) with which the subroutine is going to be called/invoked.
Local parameter
ALGEBRAIC CONCEPT
Local uniformizing parameter
In the geometry of complex algebraic curves, a local parameter for a curve C at a smooth point P is just a meromorphic function on C that has a simple zero at P. This concept can be generalized to curves defined over fields other than \mathbb{C} (or even schemes), because the local ring at a smooth point P of an algebraic curve C (defined over an algebraically closed field) is always a discrete valuation ring.
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}.
