Divisor Theory

Authors: Edwards, Harold M.

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About this book

Man sollte weniger danach streben, die Grenzen der mathe­ matischen Wissenschaften zu erweitern, als vielmehr danach, den bereits vorhandenen Stoff aus umfassenderen Gesichts­ punkten zu betrachten - E. Study Today most mathematicians who know about Kronecker's theory of divisors know about it from having read Hermann Weyl's lectures on algebraic number theory [We], and regard it, as Weyl did, as an alternative to Dedekind's theory of ideals. Weyl's axiomatization of what he calls "Kronecker's" theory is built-as Dedekind's theory was built-around unique factor­ ization. However, in presenting the theory in this way, Weyl overlooks one of Kronecker's most valuable ideas, namely, the idea that the objective of the theory is to define greatest com­ mon divisors, not to achieve factorization into primes. The reason Kronecker gave greatest common divisors the primary role is simple: they are independent of the ambient field while factorization into primes is not. The very notion of primality depends on the field under consideration-a prime in one field may factor in a larger field-so if the theory is founded on factorization into primes, extension of the field entails a completely new theory. Greatest common divisors, on the other hand, can be defined in a manner that does not change at all when the field is extended (see §1.16). Only after he has laid the foundation of the theory of divisors does Kronecker consider factorization of divisors into divisors prime in some specified field.

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"The book presents in a modern approach a remarkable algebraic technique... Interesting for both the historian of mathematics and the working specialist."

--Zentralblatt Math

Table of contents (4 chapter)

  • A Theorem of Polynomial Algebra

    Edwards, Harold M.

    Pages 1-12

    Buy Chapter $29.95
  • The General Theory

    Edwards, Harold M.

    Pages 13-59

    Buy Chapter $29.95
  • Applications to Algebraic Number Theory

    Edwards, Harold M.

    Pages 60-84

    Buy Chapter $29.95
  • Applications to the Theory of Algebraic Curves

    Edwards, Harold M.

    Pages 85-136

    Buy Chapter $29.95
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Buy this book

eBook $89.99 net
( price for USA )
  • ISBN 978-0-8176-4977-7
  • digitally watermarked, no DRM
  • included format: PDF
  • eBooks can be used on all Reading Devices
Hardcover $119.00 net
( price for USA )
  • ISBN 978-0-8176-3448-3
  • free shipping for individuals worldwide
  • usually dispatched within 3 to 5 business days

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Bibliographic Information

Bibliographic Information
Book Title
Divisor Theory
Copyright
1990
Publisher
Birkhäuser Basel
Copyright Holder
Springer Science+Business Media, LCC
eBook ISBN
978-0-8176-4977-7
DOI
10.1007/978-0-8176-4977-7
Hardcover ISBN
978-0-8176-3448-3
Edition Number
1
Topics