Geodesic
On weakly supplemented carpets of Lie type over commutative rings
Vladikavkazskij matematičeskij žurnal, Tome 23 (2021) no. 4, pp. 28-34

Voir la notice de l'article provenant de la source Math-Net.Ru

Relationships between two hypothetical conditions for the closedness of carpets of Lie type over commutative rings are considered. The results of A. K. Gutnova and V. A. Koibaev (Vestnik of Saint Petersburg University, Mathematics. Mechanics. Astronomy, 2020) on the separation of classes of weakly supplemented and supplemented matrix carpets over fields of characteristic $0$ and $2$ are carried over to carpets of any Lie type over commutative rings even characteristic. It is established that these classes of carpets are also separated by examples of irreducible closed carpets of type $ B_l $ and $ C_l $ over nonperfect fields of characteristic $2$, parametrized by two additive subgroups, which were constructed in the work of Ya. N. Nuzhin and A. V. Stepanov (Algebra and Analysis, 2019) to obtain non-standard groups between Chevalley groups over a field and its subfield. 
@article{VMJ_2021_23_4_a2,
     author = {P. S. Badin and Ya. N. Nuzhin and E. N. Troyanskaya},
     title = {On weakly supplemented carpets of {Lie} type over commutative rings},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
     pages = {28--34},
     publisher = {mathdoc},
     volume = {23},
     number = {4},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMJ_2021_23_4_a2/}
}
TY  - JOUR
AU  - P. S. Badin
AU  - Ya. N. Nuzhin
AU  - E. N. Troyanskaya
TI  - On weakly supplemented carpets of Lie type over commutative rings
JO  - Vladikavkazskij matematičeskij žurnal
PY  - 2021
SP  - 28
EP  - 34
VL  - 23
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VMJ_2021_23_4_a2/
LA  - ru
ID  - VMJ_2021_23_4_a2
ER  - 
%0 Journal Article
%A P. S. Badin
%A Ya. N. Nuzhin
%A E. N. Troyanskaya
%T On weakly supplemented carpets of Lie type over commutative rings
%J Vladikavkazskij matematičeskij žurnal
%D 2021
%P 28-34
%V 23
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VMJ_2021_23_4_a2/
%G ru
%F VMJ_2021_23_4_a2
P. S. Badin; Ya. N. Nuzhin; E. N. Troyanskaya. On weakly supplemented carpets of Lie type over commutative rings. Vladikavkazskij matematičeskij žurnal, Tome 23 (2021) no. 4, pp. 28-34. http://geodesic.mathdoc.fr/item/VMJ_2021_23_4_a2/