Geodesic
Varieties of Two-Step Solvable Algebras of Type~(1,1)
Matematičeskie zametki, Tome 76 (2004) no. 3, pp. 409-419.

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

The structure of the set of all non-nilpotent subvarieties of the variety of two-step solvable algebras of type (1,1) is studied. An additive basis of a free metabelian (1,1)-algebra is constructed. It is proved that any identity in a non-nilpotent metabelian (1,1)-algebra of degree $\geqslant6$ is a consequence of four defining relations. 
@article{MZM_2004_76_3_a9,
     author = {S. V. Platonova},
     title = {Varieties of {Two-Step} {Solvable} {Algebras} of {Type~(1,1)}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {409--419},
     publisher = {mathdoc},
     volume = {76},
     number = {3},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2004_76_3_a9/}
}
TY  - JOUR
AU  - S. V. Platonova
TI  - Varieties of Two-Step Solvable Algebras of Type~(1,1)
JO  - Matematičeskie zametki
PY  - 2004
SP  - 409
EP  - 419
VL  - 76
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2004_76_3_a9/
LA  - ru
ID  - MZM_2004_76_3_a9
ER  - 
%0 Journal Article
%A S. V. Platonova
%T Varieties of Two-Step Solvable Algebras of Type~(1,1)
%J Matematičeskie zametki
%D 2004
%P 409-419
%V 76
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2004_76_3_a9/
%G ru
%F MZM_2004_76_3_a9
S. V. Platonova. Varieties of Two-Step Solvable Algebras of Type~(1,1). Matematičeskie zametki, Tome 76 (2004) no. 3, pp. 409-419. http://geodesic.mathdoc.fr/item/MZM_2004_76_3_a9/

[1] Dorofeev G. V., “Primer razreshimogo, no ne nilpotentnogo alternativnogo koltsa”, UMN, 15:3 (1960), 147–150 | MR

[2] Zhevlakov K. A., Slinko A. M., Shestakov I. P., Shirshov A. I., Koltsa, blizkie k assotsiativnym, Nauka, M., 1978 | Zbl

[3] Belkin V. P., “O mnogoobraziyakh pravoalternativnykh algebr”, Algebra i logika, 15:5 (1976), 491–508 | MR | Zbl

[4] Medvedev Yu. A., “Konechnaya baziruemost mnogoobrazii s dvuchlennym tozhdestvom”, Algebra i logika, 17:6 (1978), 705–726 | MR

[5] Pchelintsev S. V., “Razreshimye indeksa $2$ mnogoobraziya algebr”, Matem. sb., 115:2 (1981), 179–203 | MR | Zbl

[6] Iltyakov A. V., “Reshetka podmnogoobrazii mnogoobraziya dvukhstupenchato razreshimykh alternativnykh algebr”, Algebra i logika, 21:2 (1982), 170–177 | MR | Zbl

[7] Pchelintsev S. V., “Mnogoobraziya razreshimykh indeksa $2$ alternativnykh algebr nad polem kharakteristiki $3$”, Matem. zametki, 66:4 (1999), 556–566 | MR

[8] Nikitin A. A., “Pochti alternativnye algebry”, Algebra i logika, 13:5 (1974), 501–533 | MR | Zbl

[9] Albert A. A., “Almost alternative algebras”, Portug. Math. J., 8 (1949), 23–36 | MR | Zbl