Modules and ideals of algebras of associative type

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 i...

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Veröffentlicht in:Russian mathematics 2008-08, Vol.52 (8), p.20-27
1. Verfasser: Koreshkov, N. A.
Format: Artikel
Sprache:eng
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Zusammenfassung: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.
ISSN:1066-369X
1934-810X
DOI:10.3103/S1066369X08080033