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Non-Galois cubic fields which are Euclidean but not norm-Euclidean. (English) Zbl 0853.11084

Summary: Weinberger in 1973 has shown that under the Generalized Riemann Hypothesis for Dedekind zeta functions, an algebraic number field with infinite unit group is Euclidean if and only if it is a principal ideal domain. Using a method recently introduced by us, we give two examples of cubic fields which are Euclidean but not norm–Euclidean.

MSC:

11R16 Cubic and quartic extensions
11A05 Multiplicative structure; Euclidean algorithm; greatest common divisors
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References:

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