Geodesic
Varieties of solvable index-two alternative algebras over a field of characteristic three
Matematičeskie zametki, Tome 66 (1999) no. 4, pp. 556-566 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The subvarieties of the variety $\mathrm{Alt}_2$ of solvable index-two alternative algebras over an arbitrary field of characteristic 3 are studied. The main types of such varieties are singled out in the language of identities, and inclusions between these types are established. The main results is the following. Theorem. {\it The topological rank of the variety $\mathrm{Alt}_2$ of solvable index-two alternative algebras over an arbitrary field of characteristic $3$ is equal to five}. 
@article{MZM_1999_66_4_a10,
     author = {S. V. Pchelintsev},
     title = {Varieties of solvable index-two alternative algebras over a~field of characteristic three},
     journal = {Matemati\v{c}eskie zametki},
     pages = {556--566},
     year = {1999},
     volume = {66},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1999_66_4_a10/}
}
TY  - JOUR
AU  - S. V. Pchelintsev
TI  - Varieties of solvable index-two alternative algebras over a field of characteristic three
JO  - Matematičeskie zametki
PY  - 1999
SP  - 556
EP  - 566
VL  - 66
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/MZM_1999_66_4_a10/
LA  - ru
ID  - MZM_1999_66_4_a10
ER  - 
%0 Journal Article
%A S. V. Pchelintsev
%T Varieties of solvable index-two alternative algebras over a field of characteristic three
%J Matematičeskie zametki
%D 1999
%P 556-566
%V 66
%N 4
%U http://geodesic.mathdoc.fr/item/MZM_1999_66_4_a10/
%G ru
%F MZM_1999_66_4_a10
S. V. Pchelintsev. Varieties of solvable index-two alternative algebras over a field of characteristic three. Matematičeskie zametki, Tome 66 (1999) no. 4, pp. 556-566. http://geodesic.mathdoc.fr/item/MZM_1999_66_4_a10/

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

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

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

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

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

[6] Shestakov I. P., “Superalgebry i kontrprimery”, Sib. matem. zh., 32:6 (1991), 187–196 | MR