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A note on the characterization of CM-fields

Published online by Cambridge University Press:  09 April 2009

P. E. Blanksby  and
J. H. Loxton
P. E. Blanksby
Affiliation:
Department of Pure Mathematics The University of AdelaideAdelaideSouth Australia5001
J. H. Loxton
Affiliation:
School of Mathematics University of New South WalesKensingtonNew South Wales2033
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Abstract

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This note deals with some properties of algebraic number fields generated by numbers having all their conjugates on a circle. In particular, it is shown that an algebraic number field is a CM-field if and only if it is generated over the rationals by an element (not equal to ±1) whose conjugate all lie on the unit circle.

Subject classification (Amer. Math. Soc. (MOS) 1970): 12 A 15, 12 A 40, 14 K 22.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 26 , Issue 1 , August 1978 , pp. 26 - 30
Copyright
Copyright © Australian Mathematical Society 1978

References

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