Geodesic
Defining relations and identities of finite-dimensional nilpotent algebra $R$ with condition $dim R^{2}/R^{3} = 2$
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 13 (2016), pp. 1052-1066.

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

In this paper we describe defining relations of finite-dimensional nilpotent algebra $R$ with condition $dim R^{2}/R^{3} = 2$, it is proved that such algebra $R$ satisfies the standard identity of degree four.
Keywords: defining relations, identities, nilpotent algebra. 
@article{SEMR_2016_13_a32,
     author = {E. P. Petrov},
     title = {Defining relations and identities of finite-dimensional nilpotent algebra $R$ with condition $dim R^{2}/R^{3} = 2$},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1052--1066},
     publisher = {mathdoc},
     volume = {13},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2016_13_a32/}
}
TY  - JOUR
AU  - E. P. Petrov
TI  - Defining relations and identities of finite-dimensional nilpotent algebra $R$ with condition $dim R^{2}/R^{3} = 2$
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2016
SP  - 1052
EP  - 1066
VL  - 13
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2016_13_a32/
LA  - ru
ID  - SEMR_2016_13_a32
ER  - 
%0 Journal Article
%A E. P. Petrov
%T Defining relations and identities of finite-dimensional nilpotent algebra $R$ with condition $dim R^{2}/R^{3} = 2$
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2016
%P 1052-1066
%V 13
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2016_13_a32/
%G ru
%F SEMR_2016_13_a32
E. P. Petrov. Defining relations and identities of finite-dimensional nilpotent algebra $R$ with condition $dim R^{2}/R^{3} = 2$. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 13 (2016), pp. 1052-1066. http://geodesic.mathdoc.fr/item/SEMR_2016_13_a32/

[1] V. A. Andrunakievich (ed.), The Dniester Notebook (Unsolved problems in the theory of rings and modules), Third edition, Akad. Nauk SSSR, Sib. Otd., Inst. Mat., Novosibirsk, 1982 | MR

[2] S. A. Pikhtil'kov, On varieties generated by $n$-dimensional algebras, Manuscript deposited at VINITI, No 1213-80 Dep., Tula Polytechnic Inst., Tula, 1980

[3] Yu. N. Mal'tsev, “On identities of nilpotent algebras”, Izv. Vyssh. Uchebn. Zaved., Mat., 9 (1986), 68–72 | MR | Zbl

[4] I. L. Guseva, “On identities of finite-dimensional nilpotent algebras”, Internat. Conf. on Algebra, dedicated in the memory A. I. Mal'tsev (August 1989, Novosibirsk), 43 | Zbl

[5] E. P. Petrov, “On identities of finite-dimensional nilpotent algebras”, Algebra i Logika, 30:5 (1991), 540–556 | DOI | MR | Zbl