Algebra in superextensions of semilattices

• Date: 2018
• Main Authors: Banakh, Taras, Gavrylkiv, Volodymyr
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: semilattice; band; commutative semigroup; the space of upfamilies; the space of filters; the space of maximal linked systems; superextension; 06A12; 20M10
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/690
• Journal Title: Algebra and Discrete Mathematics

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...