๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Finite Radical Field Extensions and Crossed Homomorphisms

โœ Scribed by Toma Albu; Florin Nicolae


Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
664 KB
Volume
60
Category
Article
ISSN
0022-314X

No coin nor oath required. For personal study only.

โœฆ 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).


๐Ÿ“œ SIMILAR VOLUMES


Quartic Fields and Radical Extensions
โœ Huah Chu; Ming-chang Kang ๐Ÿ“‚ Article ๐Ÿ“… 2002 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 224 KB

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

Theoretical and Experimental Comparison
โœ Catherine S. Greenhill ๐Ÿ“‚ Article ๐Ÿ“… 1995 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 356 KB

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.

Normal Bases and Completely Free Element
โœ Dirk Hachenberger ๐Ÿ“‚ Article ๐Ÿ“… 1996 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 253 KB

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