Geodesic
On almost Engel $L$-varieties of vector spaces
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 2, pp. 1705-1713.

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

In this paper we study almost Engel $L$-varieties of vector spaces. Almost Engel $L$-varieties generated by an associative algebra considered as a vector space are described.
Mots-clés : multiplicative vector pair
Keywords: identity of pair, variety of linear algebra, $L$-variety, almost Engel variety. 
@article{SEMR_2021_18_2_a16,
     author = {A. V. Kislitsin},
     title = {On almost {Engel} $L$-varieties of vector spaces},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1705--1713},
     publisher = {mathdoc},
     volume = {18},
     number = {2},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2021_18_2_a16/}
}
TY  - JOUR
AU  - A. V. Kislitsin
TI  - On almost Engel $L$-varieties of vector spaces
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2021
SP  - 1705
EP  - 1713
VL  - 18
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2021_18_2_a16/
LA  - ru
ID  - SEMR_2021_18_2_a16
ER  - 
%0 Journal Article
%A A. V. Kislitsin
%T On almost Engel $L$-varieties of vector spaces
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2021
%P 1705-1713
%V 18
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2021_18_2_a16/
%G ru
%F SEMR_2021_18_2_a16
A. V. Kislitsin. On almost Engel $L$-varieties of vector spaces. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 2, pp. 1705-1713. http://geodesic.mathdoc.fr/item/SEMR_2021_18_2_a16/

[1] Yu.P. Razmyslov, “Finite basing of the identities of a matrix algebra of second order over a field of characteristic zero”, Algebra Logic, 12:1 (1974), 47–63 | DOI | MR | Zbl

[2] I.M. Isaev, A.V. Kislitsin, “The identities of vector spaces embedded in a linear algebra”, Sib. Èlektron. Mat. Izv., 12 (2015), 328–343 | MR | Zbl

[3] I.M. Isaev, A.V. Kislitsin, “Identities in vector spaces and examples of finite-dimensional linear algebras having no finite basis of identities”, Algebra Logic, 52:4 (2013), 290–307 | DOI | MR | Zbl

[4] A.V. Kislitsin, “The Specht property of $L$-varieties of vector spaces over an arbitrary field”, Algebra Logic, 57:5 (2018), 360–367 | DOI | MR | Zbl

[5] A.V. Kislitsin, “On nonnilpotent almost commutative $L$-varieties of vector spaces”, Sib. Math. J., 59:3 (2018), 458–462 | DOI | MR | Zbl

[6] A.R. Kemer, “The finite basis property of identities of associative algebras”, Algebra Logika, 26:5 (1987), 597–641 | DOI | MR | Zbl

[7] Yu.N. Mal'tsev, “Almost commutative varieties of associative rings”, Sib. Math. J., 17:5 (1976), 803–811 | DOI | Zbl

[8] Yu.N. Mal'tsev, “Just non commutative varieties of operator algebras and ring with some conditions on nilpotent elements”, Tamkang J. of Math., 27:1 (1996), 437–496

[9] O.B. Finogenova, “Characterizing non-matrix properties of varieties of algebras in the language of forbidden objects”, Serdica Math. J., 38:1–3 (2012), 473–496 | MR | Zbl

[10] O.B. Finogenova, “Varieties of associative algebras satisfying Engel identities”, Algebra Logic, 43:4 (2004), 271–284 | DOI | MR | Zbl

[11] O.B. Finogenova, “Almost permutative varieties of associative algebras over an infinite field”, Algebra Logic, 51:6 (2013), 519–534 | DOI | MR | Zbl

[12] O.B. Finogenova, “Almost Lie nilpotent nonprime varieties of associative algebras”, Tr. Inst. Mat. Mekh. UrO RAN, 21, no. 4, 2015, 282–291 | MR

[13] Yu.N. Mal'tsev, “On varieties of associative algebras”, Algebra Logika, 15:5 (1976), 579–584 | MR | Zbl