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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Nonunique factorization and principalization in number fields


Author: Kimball Martin
Journal: Proc. Amer. Math. Soc. 139 (2011), 3025-3038
MSC (2010): Primary 11R27, 11R29
Published electronically: May 4, 2011
MathSciNet review: 2811259
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Abstract: Following what is basically Kummer's relatively neglected approach to nonunique factorization, we determine the structure of the irreducible factorizations of an element $ n$ in the ring of integers of a number field $ K$. Consequently, we give a combinatorial expression for the number of irreducible factorizations of $ n$ in the ring. When $ K$ is quadratic, we show in certain cases how quadratic forms can be used to explicitly produce all irreducible factorizations of $ n$.


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Additional Information

Kimball Martin
Affiliation: Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73011
Email: kmartin@math.ou.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-11053-0
PII: S 0002-9939(2011)11053-0
Keywords: Nonunique factorization, principalization, class group
Received by editor(s): February 23, 2010
Published electronically: May 4, 2011
Communicated by: Matthew A. Papanikolas
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.