Geodesic
Pre-minimal pairs and homogeneous valuations
Algebra i logika, Tome 61 (2022) no. 5, pp. 541-551.

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

We offer for consideration and study the concept of a pre-minimal pair. Also we examine extensions of valuations of a field $F$ to valuations of the rational function field $F(x)$ in one variable.
Keywords: pre-mimimal pair, valuation of field. 
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Yu. L. Ershov. Pre-minimal pairs and homogeneous valuations. Algebra i logika, Tome 61 (2022) no. 5, pp. 541-551. http://geodesic.mathdoc.fr/item/AL_2022_61_5_a1/

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[2] Sudesh K. Khanduja, N. Popescu, K. W. Roggenkamp, “On minimal pairs and residually transcendental extensions of valuations”, Mathematika, 49:1/2 (2002), 93–106 | MR | Zbl

[3] Yu. L. Ershov, “Obobscheniya lemmy Genzelya i metod blizhaishego kornya”, Algebra i logika, 50:6 (2011), 701–706