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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| Published in: | Algebra and Discrete Mathematics |
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| Date: | 2004 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут прикладної математики і механіки НАН України
2004
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/156411 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862688035526672384 |
|---|---|
| author | Drozd, Y.A. Kubichka, E.A. |
| author_facet | Drozd, Y.A. Kubichka, E.A. |
| citation_txt | 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. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | 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].
|
| first_indexed | 2025-12-07T16:07:28Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-156411 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| isbn | 2000 Mathematics Subject Classification: 16G20,16G60. |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T16:07:28Z |
| publishDate | 2004 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Drozd, Y.A. Kubichka, E.A. 2019-06-18T13:27:21Z 2019-06-18T13:27:21Z 2004 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. 2000 Mathematics Subject Classification: 16G20,16G60. 1726-3255 https://nasplib.isofts.kiev.ua/handle/123456789/156411 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]. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Dimensions of finite type for representations of partially ordered sets Article published earlier |
| spellingShingle | Dimensions of finite type for representations of partially ordered sets Drozd, Y.A. Kubichka, E.A. |
| title | Dimensions of finite type for representations of partially ordered sets |
| title_full | Dimensions of finite type for representations of partially ordered sets |
| title_fullStr | Dimensions of finite type for representations of partially ordered sets |
| title_full_unstemmed | Dimensions of finite type for representations of partially ordered sets |
| title_short | Dimensions of finite type for representations of partially ordered sets |
| title_sort | dimensions of finite type for representations of partially ordered sets |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/156411 |
| work_keys_str_mv | AT drozdya dimensionsoffinitetypeforrepresentationsofpartiallyorderedsets AT kubichkaea dimensionsoffinitetypeforrepresentationsofpartiallyorderedsets |