A quadratic field which is Euclidean but not norm-Euclidean

@article{Clark1994AQF,
  title={A quadratic field which is Euclidean but not norm-Euclidean},
  author={David A. Clark},
  journal={manuscripta mathematica},
  year={1994},
  volume={83},
  pages={327-330}
}
  • D. Clark
  • Published 1 December 1994
  • Mathematics
  • manuscripta mathematica
AbstractThe classification of rings of algebraic integers which are Euclidean (not necessarily for the norm function) is a major unsolved problem. Assuming the Generalized Riemann Hypothesis, Weinberger [7] showed in 1973 that for algebraic number fields containing infinitely many units the ring of integersR is a Euclidean domain if and only if it is a principal ideal domain. Since there are principal ideal domains which are not norm-Euclidean, there should exist examples of rings of algebraic… 
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