Algebra in superextensions of groups, I: zeros and commutativity

• Date: 2018
• Main Authors: T. Banakh, T., Gavrylkiv, V., Nykyforchyn, O.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: Superextension; right-topological semigroup; 20M99; 54B20
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/815
• Journal Title: Algebra and Discrete Mathematics

Given a group \(X\) we study the algebraic structure of its superextension \(\lambda(X)\). This is a right-topological semigroup consisting of all maximal linked systems on \(X\) endowed with the operation   \(\mathcal A\circ\mathcal B=\{C\subset X:\{x\in X:x^{-1}C\in\mathcal B\}\in\mathcal A\}\)  t...