RESEARCH ARTICLE

Variants of the lattice of partitions of a countable set

Oleksandra O. Desiateryk, Olexandr G. Ganyushkin

Department of Mathematics, Kyiv University, 64, Volodymyrska st., UA-01033, Kyiv, Ukraine

Abstract: In this paper we consider the ordered by inclusion lattice $\operatorname{Part}(M)$ of all partitions of a countable set $M$. The lattice $\operatorname{Part}(M)$ is a semigroup with respect to the operation $\wedge$ which maps two partitions to their greatest lower bound. We obtain necessary and sufficiency conditions for isomorphism of two variants of the semigroup $\operatorname{Part}(M)$.

Keywords: variant, sandwich-semigroup, lattice of partitions.

MSC: 20M10, 20M14, 06B35

Received: 26.12.2016
Revised: 26.02.2018

Language: English