Tensor Algebras of Bimodules and Their Representations
DOI:
https://doi.org/10.5644/SJM.12.3.09Keywords:
Tensor algebra of a bimodule, species, (D, O)-species, hereditary rings, semiperfect rings, semidistributive rings, species of bounded representation type, rings of bounded representation type, mixed matrix problems, discrete valuation ringsAbstract
We study $(D,{\cal O})$-species, which are a special case of species introduced by Yu. A. Drozd (1980). The representations of $(D,{\cal O})$-species and modules over the corresponding tensor algebras of bimodules are considered. We find necessary and sufficient conditions on a special kind of $(D,{\cal O})$-species under which they are of bounded representation type. The conditions are given in terms of Dynkin diagrams and diagrams with weights. The connection of these $(D,{\cal O})$-species and corresponding tensor algebras with right hereditary semiperfect and semidistributive rings are studied.
* This paper was presented at the International Scientific Conference Graded structures in algebra and their applications, dedicated to the memory of Prof. Marc Krasner, IUCDubrovnik, Croatia, September, 22-24, 2016.
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