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
Finite Radical Field Extensions and Crossed Homomorphisms
โ Scribed by Toma Albu; Florin Nicolae
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 664 KB
- Volume
- 60
- Category
- Article
- ISSN
- 0022-314X
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โฆ Synopsis
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 Nicolae (J. Number Theory 52 (1995), 299 318).
๐ SIMILAR VOLUMES
An extension of composite degree over a finite field may be implemented in one or more steps, involving the implementation of zero or more intermediate fields. A comparison of the expected efficiency of different field extensions is made, using a known probabilistic algorithm to form each extension.
We continue the work of the previous paper (Hachenberger, Finite Fields Appl., in press), and, generalizing some of the results obtained there, we give explicit constructions of free and completely free elements in GF(q r n ) over GF(q), where n is any nonnegative integer and where r is any odd prim