Abstract
We study properties of n-tuple algebras of associative type. We show that the nilpotency of an n-tuple algebra 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.
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