Algebra in superextensions of semilattices
Given a semilattice X we study the algebraic properties of the semigroup υ(X) of upfamilies on X. The semigroup υ(X) contains the Stone-ˇCech extension β(X), the superextension λ(X), and the space of filters φ(X) on X as closed subsemigroups. We prove that υ(X) is a semilattice iff λ(X) is a semilat...
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| Veröffentlicht in: | Algebra and Discrete Mathematics |
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| Datum: | 2012 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут прикладної математики і механіки НАН України
2012
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/152184 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Algebra in superextensions of semilattices / T. Banakh, V. Gavrylkiv // Algebra and Discrete Mathematics. — 2012. — Vol. 13, № 1. — С. 26–42. — Бібліогр.: 14 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862709749383954432 |
|---|---|
| author | Banakh, T. Gavrylkiv, V. |
| author_facet | Banakh, T. Gavrylkiv, V. |
| citation_txt | Algebra in superextensions of semilattices / T. Banakh, V. Gavrylkiv // Algebra and Discrete Mathematics. — 2012. — Vol. 13, № 1. — С. 26–42. — Бібліогр.: 14 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | Given a semilattice X we study the algebraic properties of the semigroup υ(X) of upfamilies on X. The semigroup υ(X) contains the Stone-ˇCech extension β(X), the superextension λ(X), and the space of filters φ(X) on X as closed subsemigroups. We prove that υ(X) is a semilattice iff λ(X) is a semilattice iff φ(X) is a semilattice iff the semilattice X is finite and linearly ordered. We prove that the semigroup β(X) is a band if and only if X has no infinite antichains, and the semigroup λ(X) is commutative if and only if X is a bush with finite branches.
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| first_indexed | 2025-12-07T17:19:46Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-152184 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T17:19:46Z |
| publishDate | 2012 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Banakh, T. Gavrylkiv, V. 2019-06-08T09:42:17Z 2019-06-08T09:42:17Z 2012 Algebra in superextensions of semilattices / T. Banakh, V. Gavrylkiv // Algebra and Discrete Mathematics. — 2012. — Vol. 13, № 1. — С. 26–42. — Бібліогр.: 14 назв. — англ. 1726-3255 2010 Mathematics Subject Classification: 06A12, 20M10. https://nasplib.isofts.kiev.ua/handle/123456789/152184 Given a semilattice X we study the algebraic properties of the semigroup υ(X) of upfamilies on X. The semigroup υ(X) contains the Stone-ˇCech extension β(X), the superextension λ(X), and the space of filters φ(X) on X as closed subsemigroups. We prove that υ(X) is a semilattice iff λ(X) is a semilattice iff φ(X) is a semilattice iff the semilattice X is finite and linearly ordered. We prove that the semigroup β(X) is a band if and only if X has no infinite antichains, and the semigroup λ(X) is commutative if and only if X is a bush with finite branches. The first author has been partially financed by NCN means granted by decision DEC-2011/01/B/ST1/01439. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Algebra in superextensions of semilattices Article published earlier |
| spellingShingle | Algebra in superextensions of semilattices Banakh, T. Gavrylkiv, V. |
| title | Algebra in superextensions of semilattices |
| title_full | Algebra in superextensions of semilattices |
| title_fullStr | Algebra in superextensions of semilattices |
| title_full_unstemmed | Algebra in superextensions of semilattices |
| title_short | Algebra in superextensions of semilattices |
| title_sort | algebra in superextensions of semilattices |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/152184 |
| work_keys_str_mv | AT banakht algebrainsuperextensionsofsemilattices AT gavrylkivv algebrainsuperextensionsofsemilattices |