Non-Galois cubic fields which are Euclidean but not norm-Euclidean
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- by David A. Clark PDF
- 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.References
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Additional Information
- David A. Clark
- Affiliation: Department of Mathematics, Brigham Young University, Provo, Utah 84602
- Email: clark@math.byu.edu
- Received by editor(s): February 18, 1994
- Received by editor(s) in revised form: April 15, 1995, August 11, 1994, and February 22, 1995
- © Copyright 1996 American Mathematical Society
- Journal: Math. Comp. 65 (1996), 1675-1679
- MSC (1991): Primary 11A05; Secondary 11R16
- DOI: https://doi.org/10.1090/S0025-5718-96-00764-8
- MathSciNet review: 1355007