The Euclidean Condition in Pure Cubic and Complex Quartic Fields

@inproceedings{Cioffari2010TheEC,
  title={The Euclidean Condition in Pure Cubic and Complex Quartic Fields},
  author={Vincent G. Cioffari},
  year={2010}
}
  • Vincent G. Cioffari
  • Published 2010
In this paper we prove that a field Q( \Jd) is euclidean with respect to the ordinary norm if and only if d = 2, 3 or 10. We also prove that certain fields of the 4 /form Q(\J — d),d > 0, are or are not euclidean. The purpose of this research is to determine which pure cubic fields are euclidean with respect to the ordinary norm, and partially to determine the same for fields QA$J—d), d>0. More precisely, a field is said to be euclidean for the ordinary norm (just euclidean, for short) if its… CONTINUE READING

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