Manuscripta Mathematica a Quadratic Field Which Is Euclidean but Not Norm-euclidean

  title={Manuscripta Mathematica a Quadratic Field Which Is Euclidean but Not Norm-euclidean},
  author={David A. Clark},
The 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 integers R 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… CONTINUE READING

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