Generalized Factorization
نویسنده
چکیده
Familiarly, in Z, we have unique factorization. We investigate the general ring and what conditions we can impose on it to necessitate analogs of unique factorization. The trivial ideal structure of a field, the extent to which primary decomposition is unique, that a Noetherian ring necessarily has one, that a principal ideal domain is a unique factorization domain, and that a Dedekind domain has unique prime decomposition, are all covered. The relationship of quadratic reciprocity and the class group to the question of factorization is discussed, and Gauss’s method of computing the class number of quadratic fields and new work generalizing this to many other fields is briefly advertised.
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