• DOI:10.1090/S0002-9939-2011-11053-0
Corpus ID: 32045639

Nonunique factorization and principalization in number fields

@inproceedings{Martin2011NonuniqueFA,
  title={Nonunique factorization and principalization in number fields},
  author={Kimball Martin},
  year={2011}
}

Kimball Martin

Published 2011

Mathematics

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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.