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The Degrees of Radical Extensions

Published online by Cambridge University Press:  20 November 2018

H. D. Ursell
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The results obtained here must have been known and settled centuries ago. However, they have proved impossible to locate in the available literature. H. K. Farahat has asked for proofs of the linear independence over the rationals of certain infinite sequences of real numbers such as √2, √3, √5.... He also raised the general question of determining the degree of the field extension generated over the rationals by a family of positive irrational numbers of the form x=a1/mwhere a, m are positive integers.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 17 , Issue 4 , 01 December 1974 , pp. 615 - 617
Copyright
Copyright © Canadian Mathematical Society 1974

References

Appendix (H. K. F. 9 Feb. 1973)

1. Besikovitch, A., J. London Math. Society 15 (1940), 3-6.Google Scholar
2. Mordell, L.J., Pacific Journal of Math. 3 (1953), 625-630.Google Scholar
3. Kaplansky, I., Fields and Rings, Chicago University Press (1969) (page 60 et seq.).Google Scholar
4. Roth, R.L., American Mathematical Monthly, Vol. 78, No. 4, (1971), pp. 392-394.Google Scholar
5. Gaal, L., Classical Galois Theory with examples, Markham Publishing Co., Chicago (1971) (page 234).Google Scholar
6. American Mathematical Monthly (Comments) Vol. 78, No. 10, p. 1106 and Vol. 79, No. 10, p. 1102.Google Scholar