Some mixed matrix problems over several discrete valuation rings

Abstract

Abstract. This article presents some results about several district valuation rings with a common skew field of fractions. They are obtained from the approximation theorem for discrete valuation rings. These results give the possibility to solve basic mixed matrix problems for such rings. We present the solution of some mixed flat matrix problems over several district valuation rings with common skew field of fractions.

(D,O)-species of bounded representation type

“…and for the matrix A 3 we have the matrix problem II from [6]. By [6,Lemma 4.2], this matrix problem is of unbounded representation type.…”

“…By [6,Lemma 4.2], this matrix problem is of unbounded representation type. Therefore, the species with diagram (2.15) is of unbounded representation type.…”

Representations of (D,O)-species and flat mixed matrix problems

“…Earlier such matrix problems were considered by Gubareni [5,6], and Zavadskii and Kirichenko [7,8]. Some examples of such flat matrix problems were also considered in [9]. The reduction of the problem of description of (D,O)-species of bounded representation type to some flat mixed matrix problems is given in Section 3.…”