title: On sufficient conditions for the closure of an elementary net
metadata.name: dc.contributor.author
metadata.value: Gutnova, Alina K.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Koibaev, Vladimir A.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2020-05-28T14:06:22Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2020-05-28T14:06:22Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2020-06
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Gutnova A.K., Koibaev V.A. On sufficient conditions for the closure of an elementary net. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2020, vol. 7 (65), issue 2, pp. 230–235.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu01.2020.205
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/17932
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: An elementary net (net without a diagonal) σ = (σij )i =j of additive subgroups σij of the
  field k is called closed if the elementary net group E(σ) does not contain new elementary
  transvections. Elementary net σ = (σij) is called supplemented if for some additive
  subgroups σii of the field k the table (with diagonal) σ = (σij ), 1 ≤ i, j ≤ n, is a (full) net. Supplemented elementary nets are closed. A necessary and sufficient condition for
  the supplementarity of the elementary net σ = (σij) is the implementation of inclusions
  σijσjiσij ⊆ σij (for any i  = j). In this regard the following question is of interest (Kourovka
  notebook, question 19.63): ): is it true that for closedness of an elementary net σ = (σij)
  it suffices to execute the inclusions σ2
  ijσji ⊆ σij for any i  = j (here, by σ2
  ij we denote the
  additive subgroup of the field k generated by all squares from σij)? Elementary nets for
  which the last inclusions are satisfied we call weakly supplemented elementary nets. The
  concepts of supplemented and weakly supplemented elementary nets coincide for fields of
  odd characteristic. Thus, the aforementioned question of the sufficiency of weak supplementarity
  for the closedness of an elementary net is relevant for fields of characteristic 0
  and 2. In this article we construct examples of weakly supplemented but not supplemented
  elementary nets. An example of a closed elementary net is constructed, which is not weakly
  supplemented.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 7 (65); Issue 2
metadata.lang: -
metadata.name: dc.subject
metadata.value: nets
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: carpets
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: elementary net
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: closed net
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: supplemented net
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: elementary net group
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: transvection
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: On sufficient conditions for the closure of an elementary net
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 230-235.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/17932/1/230-235.pdf
resources.format: Adobe PDF
resources.size: 297,48 kB