Geodesic
$n$-tuple algebras of associative type
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2008), pp. 34-42 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We study properties of $n$-tuple algebras of associative type. We show that the nilpotency of an $n$-tuple algebras of associative type is determined by the nilpotency of each element. In addition, we characterize the nilpotency of an $n$-tuple algebra of associative type in terms of the trace function. In the final part of the paper, we show that a homogeneously semisimple $n$-tuple algebra of associative type is the direct sum of two-sided ideals each of which is a homogeneously simple $n$-tuple algebra of associative type.
Keywords: $n$-tuple algebra of associative type, nilpotency, homogeneous semisimple algebra, simple algebra. 
@article{IVM_2008_12_a4,
     author = {N. A. Koreshkov},
     title = {$n$-tuple algebras of associative type},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {34--42},
     year = {2008},
     number = {12},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2008_12_a4/}
}
TY  - JOUR
AU  - N. A. Koreshkov
TI  - $n$-tuple algebras of associative type
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2008
SP  - 34
EP  - 42
IS  - 12
UR  - http://geodesic.mathdoc.fr/item/IVM_2008_12_a4/
LA  - ru
ID  - IVM_2008_12_a4
ER  - 
%0 Journal Article
%A N. A. Koreshkov
%T $n$-tuple algebras of associative type
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2008
%P 34-42
%N 12
%U http://geodesic.mathdoc.fr/item/IVM_2008_12_a4/
%G ru
%F IVM_2008_12_a4
N. A. Koreshkov. $n$-tuple algebras of associative type. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2008), pp. 34-42. http://geodesic.mathdoc.fr/item/IVM_2008_12_a4/

[1] Koreshkov N. A., “O nilpotentnosti i razlozhenii algebr assotsiativnogo tipa”, Izv. vuzov. Matematika, 2006, no. 9, 34–42 | MR

[2] Bahturin Y., Zaicev M., “Identities of graded algebras”, J. Algebra, 205:1 (1998), 1–12 | DOI | MR | Zbl

[3] Bakhturin Yu. A., Zaitsev M. V., Segal S. K., “$G$-tozhdestva neassotsiativnykh algebr”, Matem. sb., 190:11 (1999), 3–14 | MR | Zbl

[4] Kertis Ch., Rainer I., Teoriya predstavlenii konechnykh grupp i assotsiativnykh algebr, Nauka, M., 1969, 668 pp. | MR