By Harold M. Edwards

guy 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. research this day so much mathematicians who learn about Kronecker's thought of divisors find out about it from having learn Hermann Weyl's lectures on algebraic quantity idea [We], and regard it, as Weyl did, instead to Dedekind's conception of beliefs. Weyl's axiomatization of what he calls "Kronecker's" thought is built-as Dedekind's idea used to be built-around specified issue ization. even if, in featuring the speculation during this means, Weyl overlooks considered one of Kronecker's Most worthy rules, specifically, the concept that the target of the speculation is to outline maximum com mon divisors, to not in achieving factorization into primes. the explanation Kronecker gave maximum universal divisors the first function is easy: they're self sufficient of the ambient box whereas factorization into primes isn't really. The very thought of primality will depend on the sphere less than consideration-a best in a single box may well consider a bigger field-so if the speculation is based on factorization into primes, extension of the sector includes a totally new idea. maximum universal divisors, nevertheless, may be outlined in a fashion that doesn't swap in any respect while the sphere is prolonged (see 1.16). merely after he has laid the basis of the speculation of divisors does Kronecker think of factorization of divisors into divisors major in a few targeted field.

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