Non-Galois cubic fields which are Euclidean but not norm-Euclidean

Clark, David

doi:10.1090/S0025-5718-96-00764-8

Non-Galois cubic fields which are Euclidean but not norm-Euclidean
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Math. Comp. 65 (1996), 1675-1679 Request permission

Abstract:

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.

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