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Real Fields and Repeated Radical Extensions

โœ Scribed by I.M. Isaacs; David Petrie Moulton

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
269 KB
Volume
201
Category
Article
ISSN
0021-8693

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Let K be a field and K(ฮฑ) be an extension field of K. If [K(ฮฑ) : K] = 3, char K = 3, and the minimal polynomial of ฮฑ over Kang (2000, Am. Math. Monthly, 107, 254-256) In this paper, we prove a similar result when [K(ฮฑ) : K] = 4, char K = 2, and the minimal polynomial of ฮฑ over K is T 4 -uT 2 -vT -w

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We extend to arbitrary finite radical extensions the results of Barrera-Mora and Velez (J. Algebra 162 (1993), 295 301) concerning simple radical extensions and we obtain in terms of crossed homomorphisms new characterizations of Kneser extensions and 2-Cogalois extensions introduced by Albu and Nic

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Let k be a real abelian number field with Galois group 2 and p an odd prime number. Denote by k the cyclotomic Z p -extension of k with Galois group 1 and by k n the nth layer of k ร‚k. Assume that the order of 2 is prime to p and that p splits completely in kร‚Q. In this article, we describe the orde