Algebra in superextensions of semilattices
Given a semilattice \(X\) we study the algebraic properties of the semigroup \(\upsilon(X)\) of upfamilies on \(X\). The semigroup \(\upsilon(X)\) contains the Stone-Cech extension \(\beta(X)\), the superextension \(\lambda(X)\), and the space of filters \(\varphi(X)\) on \(X\) as closed subsemigrou...
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Lugansk National Taras Shevchenko University
2018
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| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/690 |
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| Journal Title: | Algebra and Discrete Mathematics |
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admjournalluguniveduua-article-6902018-04-04T09:42:12Z Algebra in superextensions of semilattices Banakh, Taras Gavrylkiv, Volodymyr semilattice, band, commutative semigroup, the space of upfamilies, the space of filters, the space of maximal linked systems, superextension 06A12, 20M10 Given a semilattice \(X\) we study the algebraic properties of the semigroup \(\upsilon(X)\) of upfamilies on \(X\). The semigroup \(\upsilon(X)\) contains the Stone-Cech extension \(\beta(X)\), the superextension \(\lambda(X)\), and the space of filters \(\varphi(X)\) on \(X\) as closed subsemigroups. We prove that \(\upsilon(X)\) is a semilattice iff \(\lambda(X)\) is a semilattice iff \(\varphi(X)\) is a semilattice iff the semilattice \(X\) is finite and linearly ordered. We prove that the semigroup \(\beta(X)\) is a band if and only if \(X\) has no infinite antichains, and the semigroup \(\lambda(X)\) is commutative if and only if \(X\) is a bush with finite branches. Lugansk National Taras Shevchenko University 2018-04-04 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/690 Algebra and Discrete Mathematics; Vol 13, No 1 (2012) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/690/223 Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
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| datestamp_date |
2018-04-04T09:42:12Z |
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OJS |
| language |
English |
| topic |
semilattice band commutative semigroup the space of upfamilies the space of filters the space of maximal linked systems superextension 06A12 20M10 |
| spellingShingle |
semilattice band commutative semigroup the space of upfamilies the space of filters the space of maximal linked systems superextension 06A12 20M10 Banakh, Taras Gavrylkiv, Volodymyr Algebra in superextensions of semilattices |
| topic_facet |
semilattice band commutative semigroup the space of upfamilies the space of filters the space of maximal linked systems superextension 06A12 20M10 |
| format |
Article |
| author |
Banakh, Taras Gavrylkiv, Volodymyr |
| author_facet |
Banakh, Taras Gavrylkiv, Volodymyr |
| author_sort |
Banakh, Taras |
| 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 |
| description |
Given a semilattice \(X\) we study the algebraic properties of the semigroup \(\upsilon(X)\) of upfamilies on \(X\). The semigroup \(\upsilon(X)\) contains the Stone-Cech extension \(\beta(X)\), the superextension \(\lambda(X)\), and the space of filters \(\varphi(X)\) on \(X\) as closed subsemigroups. We prove that \(\upsilon(X)\) is a semilattice iff \(\lambda(X)\) is a semilattice iff \(\varphi(X)\) is a semilattice iff the semilattice \(X\) is finite and linearly ordered. We prove that the semigroup \(\beta(X)\) is a band if and only if \(X\) has no infinite antichains, and the semigroup \(\lambda(X)\) is commutative if and only if \(X\) is a bush with finite branches. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/690 |
| work_keys_str_mv |
AT banakhtaras algebrainsuperextensionsofsemilattices AT gavrylkivvolodymyr algebrainsuperextensionsofsemilattices |
| first_indexed |
2025-12-02T15:36:39Z |
| last_indexed |
2025-12-02T15:36:39Z |
| _version_ |
1850411371661885440 |