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k-invariant nets over an algebraic extension of a field k

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Abstract

Let K be an algebraic extension of a field k, let σ = (σ ij ) be an irreducible full (elementary) net of order n ≥ 2 (respectively, n ≥ 3) over K, while the additive subgroups σ ij are k-subspaces of K. We prove that all σij coincide with an intermediate subfield P, k ⊆ P ⊆ K, up to conjugation by a diagonal matrix.

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Authors and Affiliations

  1. Southern Mathematical Institute, North Ossetian State University named after K. L. Hetagurov, Vladikavkaz, Russia

    V. A. Koibaev

  2. Siberian Federal University, Krasnoyarsk, Russia

    Ya. N. Nuzhin

Authors
  1. V. A. Koibaev
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  2. Ya. N. Nuzhin
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Corresponding author

Correspondence to V. A. Koibaev.

Additional information

The first author was supported by the Ministry of Education and Science of the Russian Federation under Open Research and Development Program 115033020013. The second author was supported by the Russian Foundation for Basic Research (Grant 16–01–00707).

Vladikavkaz; Krasnoyarsk. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 58, No. 1, pp. 143–147, January–February, 2017; DOI: 10.17377/smzh.2017.58.114.

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Koibaev, V.A., Nuzhin, Y.N. k-invariant nets over an algebraic extension of a field k . Sib Math J 58, 109–112 (2017). https://doi.org/10.1134/S0037446617010141

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  • DOI: https://doi.org/10.1134/S0037446617010141

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