Geodesic
On the join of Spechtian varieties of algebras
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 1498-1505.

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

We constructed the example of the join Spechtian varieties of algebras over a field of characteristic zero which is not finitely based.
Keywords: linear algebra, Spechtian variety, nonfinitely based variety of algebras. 
@article{SEMR_2018_15_a29,
     author = {I. M. Isaev},
     title = {On the join of {Spechtian} varieties of algebras},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1498--1505},
     publisher = {mathdoc},
     volume = {15},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2018_15_a29/}
}
TY  - JOUR
AU  - I. M. Isaev
TI  - On the join of Spechtian varieties of algebras
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2018
SP  - 1498
EP  - 1505
VL  - 15
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2018_15_a29/
LA  - ru
ID  - SEMR_2018_15_a29
ER  - 
%0 Journal Article
%A I. M. Isaev
%T On the join of Spechtian varieties of algebras
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2018
%P 1498-1505
%V 15
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2018_15_a29/
%G ru
%F SEMR_2018_15_a29
I. M. Isaev. On the join of Spechtian varieties of algebras. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 1498-1505. http://geodesic.mathdoc.fr/item/SEMR_2018_15_a29/

[1] W. Specht, “Gesetze in Ringen. I”, Mathematische Zeitschrift, 52:5 (1950), 557–589 | DOI | MR | Zbl

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

[3] G.V. Dorofeev, “Properties of the join of varieties of algebras”, Algebra i Logika, 16:1 (1977), 24–39 | DOI | MR | Zbl

[4] I.V. Lvov, “Finite-dimensional algebras with infinite bases of identities”, Sib. Math. J., 19:1 (1978), 91–99 | MR | Zbl

[5] Yu.N. Mal'tsev, V.A. Parfenov, “A nonassociative algebra having no finite basis for its laws”, Sib. Math. J., 18:6 (1977), 1420–1421 | MR | Zbl

[6] I.M. Isaev, A.V. Kislitsin, “Identities in vector spaces and examples of finite-dimensional linear algebras having no finite basis of identities”, Algebra i Logika, 52:4 (2013), 435–460 | DOI | MR | Zbl

[7] O.V. Shashkov, “The join of varieties with associative-commutative intersection of bounded index”, Sib. Math. J., 56:3 (2015), 704–714 | DOI | MR | Zbl

[8] S.V. Polin, “Identities of finite algebras”, Sib. Math. J., 17:6 (1976), 1356–1366 | MR | Zbl

[9] A.V. Kislitsin, “On identities of spaces of linear transformations over infinite field”, Izv. Altai State Univ., 1–2(65) (2010), 37–41