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Название: An Invitation to Algebraic Numbers and Algebraic Functions
Автор: Franz Halter-Koch
Издательство: CRC Press
Год: 2020
Формат: PDF
Страниц: 595
Размер: 10,77 МБ
Язык: English
The author offers a thorough presentation of the classical theory of algebraic numbers and algebraic functions which both in its conception and in many details differs from the current literature on the subject. The basic features are: Field-theoretic preliminaries and a detailed presentation of Dedekind’s ideal theory including non-principal orders and various types of class groups; the classical theory of algebraic number fields with a focus on quadratic, cubic and cyclotomic fields; basics of the analytic theory including the prime ideal theorem, density results and the determination of the arithmetic by the class group; a thorough presentation of valuation theory including the theory of difference, discriminants, and higher ramification.