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Mat. Sb., 1999, Volume 190, Number 6, Pages 59–82 (Mi msb412)  

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

Abstract: 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.

DOI: https://doi.org/10.4213/sm412

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English version:
Sbornik: Mathematics, 1999, 190:6, 835–858

Bibliographic databases:

UDC: 512.55+512.64
MSC: Primary 15A33; Secondary 11C20, 16G20, 16W60
Received: 16.02.1998

Citation: 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
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\paper A~matrix problem over a~discrete valuation ring
\jour Mat. Sb.
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\vol 190
\issue 6
\pages 59--82
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\issue 6
\pages 835--858
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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  crossref  zmath  isi  scopus  scopus
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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