Geodesic
On graphs that are not equationally Noetherian
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 2, pp. 580-587.

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

The goal of the paper is to describe all equationally noetherian graphs in terms of forbidden subgraphs for the categories of simple graphs and graphs with loops.
Keywords: simple graphs, graphs with loops, graph groups, equationally noetherian
Mots-clés : one variable equations. 
@article{SEMR_2023_20_2_a0,
     author = {I. M. Buchinskiy and A. V. Treyer},
     title = {On graphs that are not equationally {Noetherian}},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {580--587},
     publisher = {mathdoc},
     volume = {20},
     number = {2},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2023_20_2_a0/}
}
TY  - JOUR
AU  - I. M. Buchinskiy
AU  - A. V. Treyer
TI  - On graphs that are not equationally Noetherian
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2023
SP  - 580
EP  - 587
VL  - 20
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2023_20_2_a0/
LA  - ru
ID  - SEMR_2023_20_2_a0
ER  - 
%0 Journal Article
%A I. M. Buchinskiy
%A A. V. Treyer
%T On graphs that are not equationally Noetherian
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2023
%P 580-587
%V 20
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2023_20_2_a0/
%G ru
%F SEMR_2023_20_2_a0
I. M. Buchinskiy; A. V. Treyer. On graphs that are not equationally Noetherian. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 2, pp. 580-587. http://geodesic.mathdoc.fr/item/SEMR_2023_20_2_a0/

[1] E. Daniyarova, A. Myasnikov, V. Remeslennikov, Algebraic geometry over algebraic systems, Publishing House of SB RAS, Novosibirsk, 2016

[2] E. Daniyarova, A. Myasnikov, V. Remeslennikov, “Unification theorems in algebraic geometry”, Aspects of infinite groups. A Festschrift in honor of Anthony Gaglione, eds. Fine Benjamin et al., World Scientific, Hackensack, 2008, 80–111 | DOI | MR | Zbl

[3] E. Daniyarova, A. Myasnikov, V. Remeslennikov, “Algebraic geometry over algebraic structures. II: Foundations”, J. Math. Sci., New York, 185:3 (2012), 389–416 | DOI | MR | Zbl

[4] G. Baumslag, A. Myasnikov, V. Roman'kov, “Two theorems about equationally Noetherian groups”, J. Algebra, 194:2 (1997), 654–664 | DOI | MR | Zbl

[5] G. Baumslag, A. Myasnikov, V. Remeslennikov, “Algebraic geometry over groups I: Algebraic sets and ideal theory”, J. Algebra, 219:1 (1999), 16–79 | DOI | MR | Zbl

[6] M. Shahryary, A. Shevlyakov, “Direct products, varieties, and compactness conditions”, Groups Complex. Cryptol., 9:2 (2017), 159–166 | MR | Zbl

[7] Ch.K. Gupta, N.S. Romanovskii, “The property of being equationally Noetherian for some soluble groups”, Algebra Logic, 46:1 (2007), 28–36 | DOI | MR | Zbl

[8] M.V. Kotov, “Several remarks on equationally Noetherian property”, Vestnik Omskogo universiteta, 2013:2 (2013), 24–28

[9] R. Diestel, Graph theory, Springer, Berlin, 1996 | MR | Zbl

[10] N.G. de Bruijn, P. Erdős, “A colour problem for infinite graphs and a problem in the theory of relations”, Nederl. Akad. Wet., Proc., Ser. A, 54 (1951), 371–373 | MR | Zbl