Geodesic
On the $\gamma$-classical varieties
Fundamentalʹnaâ i prikladnaâ matematika, Tome 8 (2002) no. 3, pp. 887-910.

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

We study a $\gamma$-classical varieties of associative algebras with trace. They were introduced by A. R. Kemer. It is proven that in case of characteristic $p>0$ there exists only a finite number of minimal $\gamma$-classical varieties. The basises of identities of these varieties are described. We also consruct new examples of prime varieties in positive characteristic using a new notion of convolution. 
@article{FPM_2002_8_3_a14,
     author = {L. M. Samoilov},
     title = {On the $\gamma$-classical varieties},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {887--910},
     publisher = {mathdoc},
     volume = {8},
     number = {3},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2002_8_3_a14/}
}
TY  - JOUR
AU  - L. M. Samoilov
TI  - On the $\gamma$-classical varieties
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2002
SP  - 887
EP  - 910
VL  - 8
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FPM_2002_8_3_a14/
LA  - ru
ID  - FPM_2002_8_3_a14
ER  - 
%0 Journal Article
%A L. M. Samoilov
%T On the $\gamma$-classical varieties
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2002
%P 887-910
%V 8
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FPM_2002_8_3_a14/
%G ru
%F FPM_2002_8_3_a14
L. M. Samoilov. On the $\gamma$-classical varieties. Fundamentalʹnaâ i prikladnaâ matematika, Tome 8 (2002) no. 3, pp. 887-910. http://geodesic.mathdoc.fr/item/FPM_2002_8_3_a14/

[1] Dzheims G., Teoriya predstavlenii $\mathrm S_n$, Mir, M., 1982 | MR

[2] Kash F., Moduli i koltsa, Mir, M., 1981 | MR

[3] Kemer A., “Multilinear identities of the algebras over a field of characteristic $p$”, Intern. J. of Algebra and Computations, 5:2 (1995), 189–197 | DOI | MR | Zbl

[4] Kemer A., “Remarks on the prime varieties”, Israel J. of Math., 96 (1996), 341–356 | DOI | MR | Zbl

[5] Kemer A., “On the multilinear components of the regular prime varieties”, Methods in Ring. Proc. of Trento Conferencs, Lect. Notes in Pure and Appl. Math., 198, 1998, 171–183 | MR | Zbl

[6] Kertis Ch., Rainer I., Teoriya predstavlenii konechnykh grupp i assotsiativnykh algebr, Nauka, M., 1969 | MR

[7] Razmyslov Yu. P., Tozhdestva algebr i ikh predstavlenii, Nauka, M., 1989 | MR | Zbl

[8] Samoilov L. M., “Novoe dokazatelstvo teoremy Yu. P. Razmyslova o tozhdestvakh so sledom matrichnykh superalgebr”, Fundam. i prikl. mat., 6:4 (2000), 1221–1227 | MR | Zbl