Nonexcellence of certain field extensions
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 14, Tome 338 (2006), pp. 213-226
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Consider towers of fields $F_1\subset F_2\subset F_3$, where $F_3/F_2$ is a quadratic extension and $F_2/F_1$ is an extension, which is either quadratic, or of odd degree, or purely transcendental of degree 1. We construct numerous examples of the above types such that the extension $F_3/F_1$ is not $4$-excellent. Also we show that if $k$ is a field, $\operatorname{char}k\ne2$ and $l/k$ is an arbitrary field extension of forth degree, then there exists a field extension $F/k$ such that the forth degree extension $lF/F$ is not 4-excellent.
@article{ZNSL_2006_338_a9,
author = {A. S. Sivatski},
title = {Nonexcellence of certain field extensions},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {213--226},
year = {2006},
volume = {338},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2006_338_a9/}
}
A. S. Sivatski. Nonexcellence of certain field extensions. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 14, Tome 338 (2006), pp. 213-226. http://geodesic.mathdoc.fr/item/ZNSL_2006_338_a9/
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