Abstract
In this paper, we study some properties of algebras of associative type introduced in previous papers of the author. We show that a finite-dimensional algebra of associative type over a field of zero characteristic is homogeneously semisimple if and only if a certain form defined by the trace form is nonsingular. For a subclass of algebras of associative type, it is proved that any module over a semisimple algebra is completely reducible. We also prove that any left homogeneous ideal of a semisimple algebra of associative type is generated by a homogeneous idempotent.
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Original Russian Text © N.A. Koreshkov, 2008, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2008, No. 8, pp. 25–34.
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Koreshkov, N.A. Modules and ideals of algebras of associative type. Russ Math. 52, 20–27 (2008). https://doi.org/10.3103/S1066369X08080033
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DOI: https://doi.org/10.3103/S1066369X08080033