- p-adic valuation
- мат. р-адическое нормирование
Большой англо-русский и русско-английский словарь. 2001.
p-adic valuation
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Valuation (mathematics) — Valuation in mathematics may refer to: *Valuation (algebra) *Valuation (logic) *Valuation (measure theory) * p adic valuationee also*Valuation … 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 size or multiplicity of elements of the field. They generalize to commutative algebra the notion of size… … Wikipedia
Valuation ring — In abstract algebra, a valuation ring is an integral domain D such that for every element x of its field of fractions F , at least one of x or x 1 belongs to D .Given a field F , if D is a subring of F such that either x or x 1 belongs to D for… … Wikipedia
P-adic order — In number theory, for a given prime number p , the p adic order or additive p adic valuation of a number n is the highest exponent ν such that p ν divides n . It is commonly abbreviated ord p ( n ) or ν p ( n ). The most important application of… … Wikipedia
p-adic order — In number theory, for a given prime number p, the p adic order or additive p adic valuation of a number n is the highest exponent ν such that pν divides n. It is commonly abbreviated νp(n). The most important application of the p adic order is in … Wikipedia
Discrete valuation — In mathematics, a discrete valuation is an integer valuation on a field k, that is a function satisfying the conditions . Note that often the trivial valuation which takes on only the values … 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… … Wikipedia
p-adic number — In mathematics, and chiefly number theory, the p adic number system for any prime number p extends the ordinary arithmetic of the rational numbers in a way different from the extension of the rational number system to the real and complex number… … Wikipedia
P-adic number — In mathematics, the p adic number systems were first described by Kurt Hensel in 1897 [cite journal | last = Hensel | first = Kurt | title = Über eine neue Begründung der Theorie der algebraischen Zahlen | journal =… … Wikipedia
p-adic Hodge theory — In mathematics, p adic Hodge theory is a theory that provides a way to classify and study p adic Galois representations of characteristic 0 local fields[1] with residual characteristic p (such as Qp). The theory has its beginnings in Jean Pierre… … Wikipedia
p-adically closed field — In mathematics, a p adically closed field is a field that enjoys a closure property that is a close analogue for p adic fields to what real closure is to the real field. They were introduced by James Ax and Simon B. Kochen in 1965.[1] Contents 1… … Wikipedia
