Algebra in superextensions of semilattices

• Published in: Algebra and Discrete Mathematics
• Date: 2012
• Main Authors: Banakh, T., Gavrylkiv, V.
• Format: Article
• Language: English
• Published: Інститут прикладної математики і механіки НАН України 2012
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/152184
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Algebra in superextensions of semilattices / T. Banakh, V. Gavrylkiv // Algebra and Discrete Mathematics. — 2012. — Vol. 13, № 1. — С. 26–42. — Бібліогр.: 14 назв. — англ.

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...