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Algebra and Discrete Mathematics, 2004, Issue 3, Pages 21–37 (Mi adm346)  

This article is cited in 1 scientific paper (total in 1 paper)

RESEARCH ARTICLE

Dimensions of finite type for representations of partially ordered sets

Yuriy A. Drozd, Eugene A. Kubichka

Department of Mechanics and Mathematics, Kyiv Taras Shevchenko University, 01033 Kyiv, Ukraine
Full-text PDF (279 kB) Citations (1)
Abstract: We consider the dimensions of finite type of representations of a partially ordered set, i.e. such that there is only finitely many isomorphism classes of representations of this dimension. We give a criterion for a dimension to be of finite type. We also characterize those dimensions of finite type, for which there is an indecomposable representation of this dimension, and show that there can be at most one indecomposable representation of any dimension of finite type. Moreover, if such a representation exists, it only has scalar endomorphisms. These results (Theorem 1.6, page 25) generalize those of [5,1,9].
Keywords: Representations of posets, finite type, indecomposable representations.
Bibliographic databases:
Document Type: Article
MSC: 16G20,16G60
Language: English
Citation: Yuriy A. Drozd, Eugene A. Kubichka, “Dimensions of finite type for representations of partially ordered sets”, Algebra Discrete Math., 2004, no. 3, 21–37
Citation in format AMSBIB
\Bibitem{DroKub04}
\by Yuriy~A.~Drozd, Eugene~A.~Kubichka
\paper Dimensions of finite type for representations of partially ordered sets
\jour Algebra Discrete Math.
\yr 2004
\issue 3
\pages 21--37
\mathnet{http://mi.mathnet.ru/adm346}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2146102}
\zmath{https://zbmath.org/?q=an:1067.16020}
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  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Algebra and Discrete Mathematics
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