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. 
@article{IVM_2008_8_a2,
     author = {N. A. Koreshkov},
     title = {Modules and ideals of algebras of associative type},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {25--34},
     publisher = {mathdoc},
     number = {8},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2008_8_a2/}
}
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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/