Geodesic
Stable valued fields
Algebra i logika, Tome 46 (2007) no. 6, pp. 707-728

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

We are concerned with a class of valued fields, called stable. We propound an extension of a notion in the monograph by S. Bosch, U. Güntzer, and R. Remmert (Non-Archimedean Analysis. A Systematic Approach to Rigid Analytic Geometry, Springer, Berlin (1984)), namely, that of a (ultrametric) norm on groups, rings, algebras, and vector spaces, to the case where the value of the norm is taken from an arbitrary (not necessarily Archimedean) linearly ordered Abelian group (using — as in the general theory of valuations — the version of a logarithmic norm). Our main result extends Proposition 6 in the cited monograph to the general case, thereby making it possible to use the technique of Cartesian spaces to deliver further results on stable valued fields.
Keywords: valued field, defect, stable valued field. 
@article{AL_2007_46_6_a2,
     author = {Yu. L. Ershov},
     title = {Stable valued fields},
     journal = {Algebra i logika},
     pages = {707--728},
     publisher = {mathdoc},
     volume = {46},
     number = {6},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2007_46_6_a2/}
}
TY  - JOUR
AU  - Yu. L. Ershov
TI  - Stable valued fields
JO  - Algebra i logika
PY  - 2007
SP  - 707
EP  - 728
VL  - 46
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AL_2007_46_6_a2/
LA  - ru
ID  - AL_2007_46_6_a2
ER  - 
%0 Journal Article
%A Yu. L. Ershov
%T Stable valued fields
%J Algebra i logika
%D 2007
%P 707-728
%V 46
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AL_2007_46_6_a2/
%G ru
%F AL_2007_46_6_a2
Yu. L. Ershov. Stable valued fields. Algebra i logika, Tome 46 (2007) no. 6, pp. 707-728. http://geodesic.mathdoc.fr/item/AL_2007_46_6_a2/