arXiv 1102.22552011-02-10math.NT

Non-unique factorization and principalization in number fields

Kimball Martin

备注：: to appear in Proceedings of the AMS
发表信息：: Proc. Amer. Math. Soc., Vol 139, No 9 (2011), 3025-3038

英文摘要：

We give a precise description of how the class group of a number field measures the failure of unique factorization in its ring of integers. Specifically, following ideas of Kummer, we determine the structure of all irreducible factorizations of an element in the ring of integers of a number field, and give a combinatorial description for the number of such factorizations. In certain cases, we show how quadratic forms can explicitly provide all such factorizations.

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