On representation type of a pair of posets with involution
In this paper we consider the problem on classifying the representations of a pair of posets with involution. We
 prove that if one of these is a chain of length at least 4 with trivial
 involution and the other is with nontrivial one, then the pair is
 tame ⇔ it is of finite...
Gespeichert in:
| Veröffentlicht in: | Algebra and Discrete Mathematics |
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| Datum: | 2005 |
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут прикладної математики і механіки НАН України
2005
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/156608 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | On representation type of a pair of posets with involution / V.M. Bondarenko // Algebra and Discrete Mathematics. — 2005. — Vol. 4, № 1. — С. 1–7. — Бібліогр.: 12 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | In this paper we consider the problem on classifying the representations of a pair of posets with involution. We
prove that if one of these is a chain of length at least 4 with trivial
involution and the other is with nontrivial one, then the pair is
tame ⇔ it is of finite type ⇔ the poset with nontrivial involution
is a ∗-semichain (∗ being the involution). The case that each of the
posets with involution is not a chain with trivial one was considered by the author earlier. In proving our result we do not use the
known technically difficult results on representation type of posets
with involution.
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| ISSN: | 1726-3255 |