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Journal of Siberian Federal University. Mathematics & Physics, 2019, Volume 12, Issue 6, Pages 728–735
DOI: https://doi.org/10.17516/1997-1397-2019-12-6-728-735
(Mi jsfu803)
 

This article is cited in 1 scientific paper (total in 1 paper)

Elementary nets (carpets) over a discrete valuation ring

Vladimir A. Koibaevab

a North-Ossetian State University, Vatutina, 44-46, Vladikavkaz, 362025, Russia
b SMI VSC RAS, Markusa, 22, Vladikavkaz, 362027, Russia
Full-text PDF (120 kB) Citations (1)
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Abstract: Elementary net (carpet) σ=(σij) is called closed (admissible) if the elementary net (carpet) group E(σ) does not contain a new elementary transvections. The work is related to the question of V. M. Levchuk 15.46 from the Kourovka notebook( closedness (admissibility) of the elementary net (carpet)over a field). Let R be a discrete valuation ring, K be the field of fractions of R, σ=(σij) be an elementary net of order n over R, ω=(ωij) be a derivative net for σ, and ωij is ideals of the ring R. It is proved that if K is a field of odd characteristic, then for the closedness (admissibility) of the net σ, the closedness (admissibility) of each pair (σij,σji) is sufficient for all ij.
Keywords: nets, carpets, elementary net, closed net, derivative net, elementary net group, transvections, discrete valuation ring.
Received: 24.06.2019
Received in revised form: 16.08.2019
Accepted: 20.09.2019
Bibliographic databases:
Document Type: Article
UDC: 512.5
Language: English
Citation: Vladimir A. Koibaev, “Elementary nets (carpets) over a discrete valuation ring”, J. Sib. Fed. Univ. Math. Phys., 12:6 (2019), 728–735
Citation in format AMSBIB
\Bibitem{Koi19}
\by Vladimir~A.~Koibaev
\paper Elementary nets (carpets) over a discrete valuation ring
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2019
\vol 12
\issue 6
\pages 728--735
\mathnet{http://mi.mathnet.ru/jsfu803}
\crossref{https://doi.org/10.17516/1997-1397-2019-12-6-728-735}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000501590600009}
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  • https://www.mathnet.ru/eng/jsfu/v12/i6/p728
  • This publication is cited in the following 1 articles:
    1. V. A. Koibaev, “Closed elementary nets over a field of characteristic 0”, Siberian Math. J., 62:2 (2021), 262–266  mathnet  crossref  crossref  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Журнал Сибирского федерального университета. Серия "Математика и физика"
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    Abstract page:219
    Full-text PDF :39
    References:32
     
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