Variants of a lattice of partitions of a countable set

• Дата: 2018
• Автори: Desiateryk, Oleksandra, Ganyushkin, Olexandr
• Формат: Стаття
• Мова: English
• Опубліковано: Lugansk National Taras Shevchenko University 2018
• Теми: variant; sandwich-semigroup; lattice of partitions; 20M10; 20M14; 06B35
• Онлайн доступ: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/373
• Назва журналу: Algebra and Discrete Mathematics

In this paper we consider the ordered by inclusion lattice \(\text{Part}(M)\) of all partitions of a countable set \(M\). The lattice \(\text{Part}(M)\) is a semigroup with respect to the operation \(\wedge\) which maps two partitions to their greatest lower bound. We obtain necessary and sufficienc...