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What (who) is valuation ideal - definition
FUNCTION IN ALGEBRA
Dedekind valuation; Valuation theory; Exponential valuation; Valued field; Complete valued field; Valuation group; Valuation ring of a valuation; Prime ideal of a valuation; Maximal ideal of a valuation; Residue field of a valuation; Value group; P-adic valuation of a Dedekind domain; Trivial valuation; Equivalence of valuations; Extension of a valuation; Reduced ramification index of an extension of valuations; Ramification index of an extension of valuations; Relative degree of an extension of valuations; Krull valuation
ideal
WIKIMEDIA DISAMBIGUATION PAGE
Ideal (mathematics); Ideals; Ideal (disambiguation)
<theory> In domain theory, a non-empty, downward closed
subset which is also closed under binary least upper bounds.
I.e. anything less than an element is also an element and the
least upper bound of any two elements is also an element.
(1997-09-26)
ideal
WIKIMEDIA DISAMBIGUATION PAGE
Ideal (mathematics); Ideals; Ideal (disambiguation)
I. a.
1.
Intellectual, mental.
2.
Imaginary, unreal, fanciful, fantastic, fancied, illusory, chimerical, visionary, shadowy.
3.
Complete, perfect, consummate, filling our utmost conceptions.
II. n.
Imaginary standard, ideal model of perfection.
IDEAL
WIKIMEDIA DISAMBIGUATION PAGE
Ideal (mathematics); Ideals; Ideal (disambiguation)
1. Ideal DEductive Applicative Language. A language by Pier
Bosco and Elio Giovannetti combining Miranda and Prolog.
Function definitions can have a guard condition (introduced
by ":-") which is a conjunction of equalities between
arbitrary terms, including functions. These guards are solved
by normal Prolog resolution and unification. It was
originally compiled into C-Prolog but was eventually to be
compiled to K-leaf.
2. A numerical constraint language written by Van Wyk of
Stanford in 1980 for typesetting graphics in documents.
It was inspired partly by Metafont and is distributed as
part of Troff.
["A High-Level Language for Specifying Pictures", C.J. Van
Wyk, ACM Trans Graphics 1(2):163-182 (Apr 1982) ].
(1994-12-15)
Wikipedia
Valuation (algebra)
In algebra (in particular in algebraic geometry or algebraic number theory), a valuation is a function on a field that provides a measure of the size or multiplicity of elements of the field. It generalizes to commutative algebra the notion of size inherent in consideration of the degree of a pole or multiplicity of a zero in complex analysis, the degree of divisibility of a number by a prime number in number theory, and the geometrical concept of contact between two algebraic or analytic varieties in algebraic geometry. A field with a valuation on it is called a valued field.
