Translation for 'algebraic number theory' from English to Russian

algebraic number theory

алгебраическая теория {ж} чиселмат.

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algebraic number

алгебраическое число {с}мат.

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number theory

теория {ж} чиселмат.

algebraic

алгебраический {adj}мат.

algebraic expression

алгебраическое выражение {с}мат.

algebraic geometry

алгебраическая геометрия {ж}мат.наука

algebraic curve

алгебраическая кривая {ж}мат.

algebraic structure

алгебраическая структура {ж}мат.

theory

теория {ж}

ring theory

теория {ж} колецмат.

set theory

теория {ж} множествмат.

M-theory

М-теория {ж}физ.

economic theory

экономическая теория {ж}наукаэкон.

knot theory

теория {ж} узловмат.

in theory

теоретически {adv}

game theory

теория {ж} игрмат.

conspiracy theory

теория {ж} заговорапол.псих.социол.

конспирологическая теория {ж}пол.псих.социол.

control theory

теория {ж} управленияинж.мат.

special theory of relativity <STR>

специальная теория {ж} относительности <СТО>физ.

number

число {с}мат.

• of the rational numbers are called algebraic number fields and are the main objects of study of algebraic number theory.
• Many areas of mathematics and computer science have been brought to bear on the problem, including elliptic curves, algebraic number theory, and quantum computing.
• Global fields are in the limelight in algebraic number theory and arithmetic geometry.
• Hilbert unified the field of algebraic number theory with his 1897 treatise "Zahlbericht" (literally "report on numbers").
• In algebraic number theory, Dirichlet's theorem generalizes to Chebotarev's density theorem.

• In algebraic number theory, the study of Diophantine equations led mathematicians, during 19th century, to introduce generalizations of the integers called algebraic integers.
• The unsolved problem stimulated the development of algebraic number theory in the 19th century, and the proof of the modularity theorem in the 20th century.
• This paper not only introduced the Gaussian integers and proved they are a unique factorization domain, it also introduced the terms norm, unit, primary, and associate, which are now standard in algebraic number theory.
• of "A" under extension is one of the central problems of algebraic number theory.
• Number theory includes several subareas, including analytic number theory, algebraic number theory, geometry of numbers (method oriented), diophantine equations, and transcendence theory (problem oriented).

• The notational convenience of the Legendre symbol inspired introduction of several other "symbols" used in algebraic number theory, such as the Hilbert symbol and the Artin symbol.
• In contrast, one of the basic theorems in algebraic number theory asserts that the class group of the ring of integers of a number field is finite; its cardinality is called the class number and it is an important and rather mysterious invariant, notwithstanding the hard work of many leading mathematicians from Gauss to the present day.