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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 at the present time such a lot mathematicians who find out about Kronecker's thought of divisors learn about it from having learn Hermann Weyl's lectures on algebraic quantity conception [We], and regard it, as Weyl did, in its place to Dedekind's idea of beliefs. Weyl's axiomatization of what he calls "Kronecker's" thought is built-as Dedekind's conception was once built-around distinct issue ization. despite the fact that, in offering the idea during this manner, Weyl overlooks considered one of Kronecker's Most worthy rules, particularly, the concept that the target of the speculation is to outline maximum com mon divisors, to not in attaining factorization into primes. the explanation Kronecker gave maximum universal divisors the first position is straightforward: they're self sustaining of the ambient box whereas factorization into primes isn't really. The very concept of primality will depend on the sphere lower than consideration-a major in a single box might consider a bigger field-so if the speculation is based on factorization into primes, extension of the sector involves a totally new idea. maximum universal divisors, however, may be outlined in a way that doesn't switch in any respect whilst the sphere is prolonged (see 1.16). in basic terms after he has laid the root of the speculation of divisors does Kronecker think about factorization of divisors into divisors best in a few targeted box.

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