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On totally complex quartic fields with small discriminants

Published online by Cambridge University Press:  24 October 2008

H. J. Godwin
H. J. Godwin
Affiliation:
University College, Swansea
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Extract

A table of totally complex quartic fields, with small discriminants, which possess quadratic subfields was given by Delone and Faddeev(1); the purpose of the present paper is to give a table of such fields which have no subfield. The method used is based on an idea used recently (2) in the case of totally real quartic fields and depends on a special case of the following theorem, which is stated in full generality.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 53 , Issue 1 , January 1957 , pp. 1 - 4
Copyright
Copyright © Cambridge Philosophical Society 1957

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References

REFERENCES

(1)Delone, B. N. and Faddeev, D. K.Theory of irrationalities of the third degree. Acad. Sci. URSS Trav. Inst. Math. Stekloff, 11 (1940) (Russian).Google Scholar
(2)Godwin, H. J.J. Lond. Math. Soc. 31 (1956), 478–485.CrossRefGoogle Scholar
(3)Sommer, J.Introduction à la Théorie des Nombres algébriques (Paris, 1911).Google Scholar