• Corpus ID: 238253166

On the existence of euclidean ideal class in quadratic, cubic and quartic extensions

@inproceedings{Krishnamoorthy2021OnTE,
  title={On the existence of euclidean ideal class in quadratic, cubic and quartic extensions},
  author={Srilakshmi Krishnamoorthy and Sunil Kumar Pasupulati},
  year={2021}
}
Let K be a number field. We denote the number ring and units of K by OK and O K respectively. The class group ClK is defined as JK/PK , where JK is the group of fractional ideals and PK is the group of principal fractional ideals of K. The Hilbert class field of K is denoted by H(K). Let K/Q be an abelian extension. The conductor of K denoted as f(K) is defined to be the smallest natural number such that K ⊆ Q(ζf(K)). The conductor of H(K) is also f(K) whenever H(K)/Q is abelian. The compositum… 

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