Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 31, Tome 455 (2017), pp. 42-51
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R. Y. Dryaeva; V. A. Koibaev; Ya. N. Nuzhin. Full and elementary nets over the quotient field of a principal ideal ring. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 31, Tome 455 (2017), pp. 42-51. http://geodesic.mathdoc.fr/item/ZNSL_2017_455_a4/
@article{ZNSL_2017_455_a4,
author = {R. Y. Dryaeva and V. A. Koibaev and Ya. N. Nuzhin},
title = {Full and elementary nets over the quotient field of a~principal ideal ring},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {42--51},
year = {2017},
volume = {455},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2017_455_a4/}
}
TY - JOUR
AU - R. Y. Dryaeva
AU - V. A. Koibaev
AU - Ya. N. Nuzhin
TI - Full and elementary nets over the quotient field of a principal ideal ring
JO - Zapiski Nauchnykh Seminarov POMI
PY - 2017
SP - 42
EP - 51
VL - 455
UR - http://geodesic.mathdoc.fr/item/ZNSL_2017_455_a4/
LA - ru
ID - ZNSL_2017_455_a4
ER -
%0 Journal Article
%A R. Y. Dryaeva
%A V. A. Koibaev
%A Ya. N. Nuzhin
%T Full and elementary nets over the quotient field of a principal ideal ring
%J Zapiski Nauchnykh Seminarov POMI
%D 2017
%P 42-51
%V 455
%U http://geodesic.mathdoc.fr/item/ZNSL_2017_455_a4/
%G ru
%F ZNSL_2017_455_a4
Let $K$ be the quotient field of a principal ideal ring $R$, and $\sigma=(\sigma_{ij})$ be a full (elementary) net of order $n\geq2$ (respectively, $n\geq3$) over $K$ such that the additive subgroups $\sigma_{ij}$ are nonzero $R$-modules. It is proved that, up to conjugation by diagonal matrix, all $\sigma_{ij}$ are ideals of a fixed intermediate subring $P$, $R\subseteq P\subseteq K$.
[1] V. A. Koibaev, Ya. N. Nuzhin, “Podgruppy grupp Shevalle i koltsa Li, opredelyaemye naborom additivnykh podgrupp osnovnogo koltsa”, Fundamentalnaya i prikladnaya matematika, 18:1 (2013), 75–84 | MR
[2] V. A. Koibaev, “Elementarnye seti v lineinykh gruppakh”, Trudy IMM UrO RAN, 17, no. 4, 2011, 134–141
[3] S. K. Kuklina, A. O. Likhacheva, Ya. N. Nuzhin, “O zamknutosti kovrov lieva tipa nad kommutativnymi koltsami”, Trudy IMM UrO RAN, 21, no. 3, 2015, 192–196 | MR
