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On numbers which are differences of two conjugates over Q of an algebraic integer

Published online by Cambridge University Press:  17 April 2009

T. Zaimi
T. Zaimi
Affiliation:
King Saud University, Department of Mathematics, PO Box 2455, Riyadh 11451, Saudi Arabia
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Abstract

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We continue the investigation started by A. Dubickas of the numbers which are differences of two conjugates of an algebraic integer over the field Q of rational numbers. Mainly, we show that the cubic algebraic integers over Q with zero trace satisfy this property and we give a characterisation for those for which this property holds in their normal closure. We also prove that if a normal extension K/Q is of prime degree, then every integer of K with zero trace is a difference of two conjugates of an algebraic integer in K if and only if there exists an integer of K with trace 1.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 68 , Issue 2 , October 2003 , pp. 233 - 242
Copyright
Copyright © Australian Mathematical Society 2003

References

[1]Dubickas, A., ‘On numbers which are differences of two conjugates of an algebraic integer’, Bull. Austral. Math. Soc. 65 (2002), 439–477.CrossRefGoogle Scholar
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