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Non-galois cubic fields which are euclidean but not norm-euclidean

Author: David A. Clark
Journal: Math. Comp. 65 (1996), 1675-1679
MSC (1991): Primary 11A05; Secondary 11R16
MathSciNet review: 1355007
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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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Additional Information

David A. Clark
Affiliation: Department of Mathematics, Brigham Young University, Provo, Utah 84602

Received by editor(s): February 18, 1994
Received by editor(s) in revised form: April 15, 1995, August 11, 1994, and February 22, 1995
Article copyright: © Copyright 1996 American Mathematical Society