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1 поле p-адических чисел
Русско-английский научно-технический словарь Масловского > поле p-адических чисел
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2 поле p-адических чисел
Mathematics: field of p-adic numbersУниверсальный русско-английский словарь > поле p-адических чисел
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Field (mathematics) — This article is about fields in algebra. For fields in geometry, see Vector field. For other uses, see Field (disambiguation). In abstract algebra, a field is a commutative ring whose nonzero elements form a group under multiplication. As such it … Wikipedia
Field extension — In abstract algebra, field extensions are the main object of study in field theory. The general idea is to start with a base field and construct in some manner a larger field which contains the base field and satisfies additional properties. For… … 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 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-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
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
Glossary of field theory — Field theory is the branch of mathematics in which fields are studied. This is a glossary of some terms of the subject. (See field theory (physics) for the unrelated field theories in physics.) Definition of a field A field is a commutative ring… … Wikipedia
Algebraic number field — In mathematics, an algebraic number field (or simply number field) F is a finite (and hence algebraic) field extension of the field of rational numbers Q. Thus F is a field that contains Q and has finite dimension when considered as a vector… … Wikipedia
P-adic quantum mechanics — One may compute the energy levels for a potential well like this one.[note 1] P adic quantum mechanics is a relatively recent approach to understanding the nature of fundamental physics. It is the application of p adic analysis to quantum… … Wikipedia
Local field — In mathematics, a local field is a special type of field that is a locally compact topological field with respect to a non discrete topology.[1] Given such a field, an absolute value can be defined on it. There are two basic types of local field … Wikipedia