ABSTRACT
For Artinian rings along with the notion of finite representation type the notion of bounded representation type was considered. Recall that a right Artinian ring A is said to be of bounded representation type if there is a bound on the length of finitely generated indecomposable right A-modules. The first Brauer-Thrall conjecture says that these notions are the same. M. Auslander proved that this conjecture is true for right Artinian rings. In the notion of bounded representation type for finite dimensional algebras and Artinian rings was introduced. A right Artinian ring A is said to be of bounded representation type if there is a bound on the length of indecomposable finitely generated right A-modules. To describe (D-O)-species and right hereditary SPSD-rings of bounded representation type it will be important to consider some special mixed matrix problems.
