Dimensions of finite type for representations of partially ordered sets
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 dimensi...
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| Veröffentlicht in: | Algebra and Discrete Mathematics |
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| Datum: | 2004 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут прикладної математики і механіки НАН України
2004
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/156411 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Dimensions of finite type for representations of partially ordered sets / Y.A. Drozd, E.A. Kubichka // Algebra and Discrete Mathematics. — 2004. — Vol. 3, № 3. — С. 21–37. — Бібліогр.: 13 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | 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].
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| ISBN: | 2000 Mathematics Subject Classification: 16G20,16G60. |
| ISSN: | 1726-3255 |