Variants of a lattice of partitions of a countable set
Oleksandra Desiateryk, Olexandr Ganyushkin · The scientific electronic library of periodicals of the National Academy of Sciences of Ukraine (National Academy of Sciences of Ukraine) · 2018
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 two variants of the semigroup Part(M).