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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| Datum: | 2012 |
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| Sprache: | English |
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Інститут прикладної математики і механіки НАН України
2012
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| Schriftenreihe: | Algebra and Discrete Mathematics |
| Online Zugang: | http://dspace.nbuv.gov.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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irk-123456789-1521842019-06-09T01:25:28Z Algebra in superextensions of semilattices Banakh, T. Gavrylkiv, V. 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. 2012 Article 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. http://dspace.nbuv.gov.ua/handle/123456789/152184 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
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English |
| 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. |
| format |
Article |
| author |
Banakh, T. Gavrylkiv, V. |
| spellingShingle |
Banakh, T. Gavrylkiv, V. Algebra in superextensions of semilattices Algebra and Discrete Mathematics |
| author_facet |
Banakh, T. Gavrylkiv, V. |
| author_sort |
Banakh, T. |
| title |
Algebra in superextensions of semilattices |
| title_short |
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_sort |
algebra in superextensions of semilattices |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2012 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/152184 |
| 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. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT banakht algebrainsuperextensionsofsemilattices AT gavrylkivv algebrainsuperextensionsofsemilattices |
| first_indexed |
2025-07-13T02:29:52Z |
| last_indexed |
2025-07-13T02:29:52Z |
| _version_ |
1837497101958774784 |