Valuation (algebra)
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
In algebra (in particular in algebraic geometry or algebraic number theory), a valuation is a function on a field that provides a measure of 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.