Free \((\ell r, rr)\)-dibands

• Date: 2018
• Main Author: Zhuchok, Anatolii V.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: left (right) regular band; \((\ell r; rr)\)-diband; diband of subdimonoids; dimonoid; semigroup; 08B20; 20M10; 20M50; 17A30; 17A32
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/749
• Journal Title: Algebra and Discrete Mathematics

We prove that varieties of \((\ell r, rr)\)-dibands and \((\ell n, rn)\)-dibands coincide and describe the structure of free \((\ell r, rr)\)-dibands. We also show that operations of an idempotent dimonoid with left (right) regular bands coincide, construct a new class of dimonoids and for such dimo...