Variants of a lattice of partitions of a countable set

• Published in: Algebra and Discrete Mathematics
• Date: 2018
• Main Authors: Desiateryk, O.O., Ganyushkin, O.G.
• Format: Article
• Language: English
• Published: Інститут прикладної математики і механіки НАН України 2018
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/188370
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Variants of a lattice of partitions of a countable set / O.O. Desiateryk, O.G Ganyushkin // Algebra and Discrete Mathematics. — 2018. — Vol. 26, № 1. — С. 8–18. — Бібліогр.: 10 назв. — англ.

In this paper we consider the ordered by inclusion lattice Part(M) of all partitions of a countable set M. The lattice Part(M) is a semigroup with respect to the operation Λ which maps two partitions to their greatest lower bound. We obtain necessary and sufficiency conditions for isomorphism of tw...