# 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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