Algebraic Numbers and Algebraic Functions

Nonfiction, Science & Nature, Mathematics, Number Theory
Cover of the book Algebraic Numbers and Algebraic Functions by P.M. Cohn, CRC Press
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Author: P.M. Cohn ISBN: 9781351086486
Publisher: CRC Press Publication: January 18, 2018
Imprint: Chapman and Hall/CRC Language: English
Author: P.M. Cohn
ISBN: 9781351086486
Publisher: CRC Press
Publication: January 18, 2018
Imprint: Chapman and Hall/CRC
Language: English

This book is an introduction to the theory of algebraic numbers and algebraic functions of one variable. The basic development is the same for both using E Artin's legant approach, via valuations. Number Theory is pursued as far as the unit theorem and the finiteness of the class number. In function theory the aim is the Abel-Jacobi theorem describing the devisor class group, with occasional geometrical asides to help understanding. Assuming only an undergraduate course in algebra, plus a little acquaintance with topology and complex function theory, the book serves as an introduction to more technical works in algebraic number theory, function theory or algebraic geometry by an exposition of the central themes in the subject.

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This book is an introduction to the theory of algebraic numbers and algebraic functions of one variable. The basic development is the same for both using E Artin's legant approach, via valuations. Number Theory is pursued as far as the unit theorem and the finiteness of the class number. In function theory the aim is the Abel-Jacobi theorem describing the devisor class group, with occasional geometrical asides to help understanding. Assuming only an undergraduate course in algebra, plus a little acquaintance with topology and complex function theory, the book serves as an introduction to more technical works in algebraic number theory, function theory or algebraic geometry by an exposition of the central themes in the subject.

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