Geodesic
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

Voir la notice de l'article provenant de la source Math-Net.Ru

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},
     publisher = {mathdoc},
     volume = {338},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2006_338_a9/}
}
TY  - JOUR
AU  - A. S. Sivatski
TI  - Nonexcellence of certain field extensions
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2006
SP  - 213
EP  - 226
VL  - 338
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2006_338_a9/
LA  - ru
ID  - ZNSL_2006_338_a9
ER  - 
%0 Journal Article
%A A. S. Sivatski
%T Nonexcellence of certain field extensions
%J Zapiski Nauchnykh Seminarov POMI
%D 2006
%P 213-226
%V 338
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZNSL_2006_338_a9/
%G ru
%F 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/