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Izv. RAN. Ser. Mat., 2001, Volume 65, Issue 1, Pages 25–60 (Mi izv318)  

This article is cited in 3 scientific papers (total in 3 papers)

On the structure of two-dimensional local skew fields

A. B. Zheglov

M. V. Lomonosov Moscow State University

Abstract: The concept of $n$-dimensional local skew field is a direct generalization of the concept of $n$-dimensional local field. We study 2-dimensional local skew fields and solve the classification problem for the those of characteristic 0 whose last residue field is contained in the centre, and suggest a condition under which there is a section of the residue map whose first residue skew field is commutative. Under this condition we solve the classification problem for all 2-dimensional local skew fields.
For skew fields of characteristic 0 whose last residue field is contained in the centre, we state a criterion for two elements to be conjugate.

DOI: https://doi.org/10.4213/im318

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English version:
Izvestiya: Mathematics, 2001, 65:1, 23–55

Bibliographic databases:

MSC: 14G99, 14F10, 14J20, 11S31, 12G05, 12G10
Received: 28.06.1999

Citation: A. B. Zheglov, “On the structure of two-dimensional local skew fields”, Izv. RAN. Ser. Mat., 65:1 (2001), 25–60; Izv. Math., 65:1 (2001), 23–55

Citation in format AMSBIB
\Bibitem{Zhe01}
\by A.~B.~Zheglov
\paper On the structure of two-dimensional local skew fields
\jour Izv. RAN. Ser. Mat.
\yr 2001
\vol 65
\issue 1
\pages 25--60
\mathnet{http://mi.mathnet.ru/izv318}
\crossref{https://doi.org/10.4213/im318}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1829402}
\zmath{https://zbmath.org/?q=an:1008.12004}
\transl
\jour Izv. Math.
\yr 2001
\vol 65
\issue 1
\pages 23--55
\crossref{https://doi.org/10.1070/im2001v065n01ABEH000318}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33747136178}


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  • https://doi.org/10.4213/im318
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. V. Tikhonov, V. I. Yanchevskii, “The indices of central simple algebras over function fields of projective spaces over $P_{n,r}$-fields”, Sb. Math., 193:11 (2002), 1691–1705  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. A. B. Zheglov, “On wild division algebras over fields of power series”, Sb. Math., 195:6 (2004), 783–817  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. A. B. Zheglov, D. V. Osipov, “On Some Questions Related to the Krichever Correspondence”, Math. Notes, 81:4 (2007), 467–476  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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