Divisor Theory
Jun 2013 · Springer Science & Business Media
Ebook
166
Pages
reportRatings and reviews aren’t verified Learn More
About this ebook
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 {sect}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
Rate this ebook
Tell us what you think.
Reading information
Smartphones and tablets
Install the Google Play Books app for Android and iPad/iPhone. It syncs automatically with your account and allows you to read online or offline wherever you are.
Laptops and computers
You can listen to audiobooks purchased on Google Play using your computer's web browser.
eReaders and other devices
To read on e-ink devices like Kobo eReaders, you'll need to download a file and transfer it to your device. Follow the detailed Help Center instructions to transfer the files to supported eReaders.
