This article is cited in 16 papers

$n$-tuple algebras of associative type

N. A. Koreshkov

Kazan State University, Kazan

Abstract: 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.

UDC: 512.554

Received: 13.11.2006

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2008, 52:12, 28–35

Bibliographic databases:

• 
• 
•