On identities of right alternative metabelian Grassmann algebras
Fundamentalʹnaâ i prikladnaâ matematika, Tome 13 (2007) no. 2, pp. 157-183.

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

The right alternative metabelian (solvable of index 2) Grassmann algebras of rank 1 and 2 are studied. A basis of identities of a right alternative metabelian Grassmann algebra of rank 1 is presented. Then it is proved that the variety generated by the indicated algebra has almost finite topological rank. It is also shown that the variety generated by a Grassmann algebra of rank 2 is not Spechtian.
@article{FPM_2007_13_2_a6,
     author = {S. V. Pchelintsev},
     title = {On identities of right alternative metabelian {Grassmann} algebras},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {157--183},
     publisher = {mathdoc},
     volume = {13},
     number = {2},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2007_13_2_a6/}
}
TY  - JOUR
AU  - S. V. Pchelintsev
TI  - On identities of right alternative metabelian Grassmann algebras
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2007
SP  - 157
EP  - 183
VL  - 13
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FPM_2007_13_2_a6/
LA  - ru
ID  - FPM_2007_13_2_a6
ER  - 
%0 Journal Article
%A S. V. Pchelintsev
%T On identities of right alternative metabelian Grassmann algebras
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2007
%P 157-183
%V 13
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FPM_2007_13_2_a6/
%G ru
%F FPM_2007_13_2_a6
S. V. Pchelintsev. On identities of right alternative metabelian Grassmann algebras. Fundamentalʹnaâ i prikladnaâ matematika, Tome 13 (2007) no. 2, pp. 157-183. http://geodesic.mathdoc.fr/item/FPM_2007_13_2_a6/

[1] Bakhturin Yu. A., Tozhdestva v algebrakh Li, Nauka, M., 1985

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

[3] Drenski V. S., “O tozhdestvakh v algebrakh Li”, Algebra i logika, 13:3 (1974), 265–290 | MR | Zbl

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

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

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

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

[8] Pchelintsev S. V., “Ob odnom pochti shpekhtovom mnogoobrazii tsentralno metabelevykh alternativnykh algebr nad polem kharakteristiki 3”, Mat. sb., 191:6 (2000), 127–144 | MR | Zbl

[9] Pchelintsev S. V., “Struktura slabykh tozhdestv na grassmanovykh obolochkakh tsentralno-metabelevykh alternativnykh superalgebr superranga 1 nad polem kharakteristiki 3”, Fundament. i prikl. mat., 7:3 (2001), 849–871 | MR | Zbl

[10] Pchelintsev S. V., “Pravoalternativnye metabelevy algebry Grassmana”, XIII Mezhdunarodnaya konferentsiya “Matematika. Ekonomika. Obrazovanie”. III Mezhdunarodnyi simpozium “Ryady Fure i ikh prilozheniya”, Tezisy dokladov., Rostov-na-Donu, 2005, 87

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

[12] Shestakov I. P., “Free Malcev superalgebra on one odd generator”, J. Algebra Appl., 2:4 (2003), 451–461 | DOI | MR | Zbl

[13] Vaughan-Lee M. R., “Varieties of Lie algebras”, Quart. J. Math. Oxford Ser., 21:83 (1970), 297–308 | DOI | MR | Zbl