Email this article Full and Elementary Nets over the Quotient Field of a Principal Ideal Ring
- Authors: Dryaeva R.Y.1, Koibaev V.A.2, Nuzhin Y.N.3
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Affiliations:
- North-Ossetian State University
- North-Ossetian State University, South Mathematical Institute of the Russian Academy of Sciences
- Siberian Federal University
- Issue: Vol 234, No 2 (2018)
- Pages: 141-147
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/241786
- DOI: https://doi.org/10.1007/s10958-018-3990-y
- ID: 241786
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Abstract
Let K be the quotient field of a principal ideal ring R, and let σ = (σij) be a full (respectively, elementary) net of order n ≥ 2 (respectively, n ≥ 3) over K such that the additive subgroups σij are nonzero R-modules. It is proved that, up to conjugation by a diagonal matrix, all σij are ideals of a fixed intermediate subring P, R ⊆ P ⊆ K.
About the authors
R. Y. Dryaeva
North-Ossetian State University
Author for correspondence.
Email: dryaeva-roksana@mail.ru
Russian Federation, Vladicaucasus
V. A. Koibaev
North-Ossetian State University, South Mathematical Institute of the Russian Academy of Sciences
Email: dryaeva-roksana@mail.ru
Russian Federation, Vladicaucasus
Ya. N. Nuzhin
Siberian Federal University
Email: dryaeva-roksana@mail.ru
Russian Federation, Krasnoyarsk
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