Geodesic
Modules and ideals of algebras of associative type
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2008), pp. 25-34

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In this paper we study some properties of associative-type algebras 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. We prove the total reducedness of modulus over semisimple algebras in a certain subclass of associative-type algebras. We also prove that any left homogeneous ideal of a semisimple algebra of associative type is generated by a homogeneous idempotent.
Keywords: algebra of associative type, homogeneous semisimple algebra, modulus, ideal, homogeneous idempotent. 
N. A. Koreshkov. Modules and ideals of algebras of associative type. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2008), pp. 25-34. http://geodesic.mathdoc.fr/item/IVM_2008_8_a2/
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     title = {Modules and ideals of algebras of associative type},
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