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

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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. 
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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/

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