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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

The Euclidean condition in pure cubic and complex quartic fields


Author: Vincent G. Cioffari
Journal: Math. Comp. 33 (1979), 389-398
MSC: Primary 12A30
MathSciNet review: 514835
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Abstract: In this paper we prove that a field $ Q{(^3}\sqrt d )$ is euclidean with respect to the ordinary norm if and only if $ d = 2,3$ or 10. We also prove that certain fields of the form $ Q{(^4}\sqrt { - d} ),d > 0$, are or are not euclidean.


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DOI: http://dx.doi.org/10.1090/S0025-5718-1979-0514835-5
PII: S 0025-5718(1979)0514835-5
Article copyright: © Copyright 1979 American Mathematical Society