This article is cited in 1 scientific paper (total in 1 paper)
A matrix problem over a discrete valuation ring
A. G. Zavadskii, U. S. Revitskaya
Kiev State Technical University of Construction and Architecture
A flat matrix problem of mixed type (over a discrete valuation ring and its skew field of fractions) is considered which naturally arises in connection with several problems in the theory of integer-valued representations and in ring theory. For this problem, a criterion for module boundedness is proved, which is stated in terms of a pair of partially ordered sets $(\mathscr P(A),\mathscr P(B))$ associated with the pair of transforming algebras $(A,B)$ defining the problem. The corresponding statement coincides in effect with the formulation of Kleiner's well-known finite-type criterion for representations of pairs of partially ordered sets over a field. The proof is based on a reduction (which uses the techniques of differentiation) to representations of semimaximal rings (tiled orders) and partially ordered sets.
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Sbornik: Mathematics, 1999, 190:6, 835–858
MSC: Primary 15A33; Secondary 11C20, 16G20, 16W60
A. G. Zavadskii, U. S. Revitskaya, “A matrix problem over a discrete valuation ring”, Mat. Sb., 190:6 (1999), 59–82; Sb. Math., 190:6 (1999), 835–858
Citation in format AMSBIB
\by A.~G.~Zavadskii, U.~S.~Revitskaya
\paper A~matrix problem over a~discrete valuation ring
\jour Mat. Sb.
\jour Sb. Math.
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Moreno Canadas A. Serna R.-J. Espinosa C.-I., “on the Reduction of Some Tiled Orders”, JP J. Algebr. Number Theory Appl., 36:2 (2015), 157–176
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