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

Gubareni N.

Journal of Applied Mathematics and Computational Mechanics

2016

Vol. 15, nr 3

47--56

The problem of describing representations of (D,O)-species is reduced to flat mixed matrix problems over discrete valuation rings and their common skew field of fractions.

(D,O)-species of bounded representation type

Gubareni N.

Journal of Applied Mathematics and Computational Mechanics

2016

Vol. 15, nr 4

39--50

We describe weak (D,O)-species of bounded representation type in terms of Dynkin diagrams and diagrams with weights. We reduce the problem of their description to flat mixed matrix problems over discrete valuation rings and their common skew field of fractions.

Some mixed matrix problems over several discrete valuation rings

Gubareni N.

Journal of Applied Mathematics and Computational Mechanics

2013

Vol. 12, nr 4

47--58

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.

Valuation and discrete valuation rings

Gubareni N.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

2011

Vol. 10, nr 1

61-70

In this article we consider non-commutative valuation and discrete valuation rings. We give equivalent conditions for a ring to be a valuation and a discrete valuation ring.