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
  • 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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