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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| Опубліковано в: : | Algebra and Discrete Mathematics |
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| Дата: | 2012 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2012
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| Онлайн доступ: | 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 |
| Цитувати: | Algebra in superextensions of semilattices / T. Banakh, V. Gavrylkiv // Algebra and Discrete Mathematics. — 2012. — Vol. 13, № 1. — С. 26–42. — Бібліогр.: 14 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-152184 |
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dspace |
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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 |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Algebra in superextensions of semilattices |
| spellingShingle |
Algebra in superextensions of semilattices Banakh, T. Gavrylkiv, V. |
| 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 |
| author |
Banakh, T. Gavrylkiv, V. |
| author_facet |
Banakh, T. Gavrylkiv, V. |
| publishDate |
2012 |
| language |
English |
| container_title |
Algebra and Discrete Mathematics |
| publisher |
Інститут прикладної математики і механіки НАН України |
| format |
Article |
| 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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| issn |
1726-3255 |
| url |
https://nasplib.isofts.kiev.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. |
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AT banakht algebrainsuperextensionsofsemilattices AT gavrylkivv algebrainsuperextensionsofsemilattices |
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2025-12-07T17:19:46Z |
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2025-12-07T17:19:46Z |
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1850870843876311040 |