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Algebra Logika, 2008, Volume 47, Number 3, Pages 269–287 (Mi al359)  

This article is cited in 2 scientific papers (total in 2 papers)

Stability preservation theorems

Yu. L. Ershovab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
b Novosibirsk State University

Abstract: The basic result of the paper is the main theorem worded as follows.
Let $\mathbb F=\langle F,R\rangle$ be a valued field such that $\mathbb F_R$ has characteristic $p>0$ and let $\mathbb F_0\ge\mathbb F$ be an extension of valued fields satisfying the following conditions:
(i) there exists a set $B_0\subset R_0\setminus\mathfrak m(R_0)$ for which $\overline B_0\rightleftharpoons\{\overline b\rightleftharpoons b+\mathfrak m(R_0)\mid b\in B_0\}$ is a separating transcendence basis for a field $F_{R_0}$ over $F_R$;
(ii) $\Gamma_R$ is $p$-pure in $\Gamma_{R_0}$, i.e., $\Gamma_{R_0}/\Gamma_R$ does not contain elements of order $p$;
(iii) there exists a set $B_1\subset F^\times_0$ such that the family $\widetilde B_1\rightleftharpoons\{\widetilde b\rightleftharpoons v_{R_0}(b)+(p\Gamma_{R_0})\Gamma_R\mid b\in B_1\}$ is linearly independent in the elementary $p$-group $\Gamma_{R_0}/(p\Gamma_{R_0})\Gamma_R$;
(iv) $F_0$ is algebraic over $F(B_0\cup B_1)$.
Then the property of being stable for $\mathbb F$ implies being stable for $\mathbb F_0$.

Keywords: stable valued fiel, Henselization.

Full text: PDF file (241 kB)
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English version:
Algebra and Logic, 2008, 47:3, 155–165

Bibliographic databases:

UDC: 512.52
Received: 15.09.2007

Citation: Yu. L. Ershov, “Stability preservation theorems”, Algebra Logika, 47:3 (2008), 269–287; Algebra and Logic, 47:3 (2008), 155–165

Citation in format AMSBIB
\Bibitem{Ers08}
\by Yu.~L.~Ershov
\paper Stability preservation theorems
\jour Algebra Logika
\yr 2008
\vol 47
\issue 3
\pages 269--287
\mathnet{http://mi.mathnet.ru/al359}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2450884}
\zmath{https://zbmath.org/?q=an:1164.12005}
\transl
\jour Algebra and Logic
\yr 2008
\vol 47
\issue 3
\pages 155--165
\crossref{https://doi.org/10.1007/s10469-008-9013-1}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-49249101217}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Yu. L. Ershov, “Two Theorems on Defect-Freeness for Cyclic Extensions”, Siberian Adv. Math., 18:1 (2008), 30–43  mathnet  crossref  mathscinet
    2. Yu. L. Ershov, “A stability criterion”, Algebra and Logic, 51:2 (2012), 128–130  mathnet  crossref  mathscinet  zmath  isi
  • Алгебра и логика Algebra and Logic
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