Variants of a lattice of partitions of a countable set - Desiateryk, O.O.; Ganyushkin, O.G. (Algebra and Discrete Mathematics, 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).