Geodesic
$n$-tuple algebras of associative type
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2008), pp. 34-42

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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},
     publisher = {mathdoc},
     number = {12},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2008_12_a4/}
}
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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/