Certain verbal congruences on the free trioid
Loday and Ronco introduced the notion of a trioid as an algebra defined on a set with three binary associative operations. Every trialgebra is a linear analog of a trioid. Our paper is devoted to the study of verbal congruences on trioids. We characterize the least abelian dimonoid congruences, the...
Збережено в:
| Дата: | 2024 |
|---|---|
| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2024
|
| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2274 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| Резюме: | Loday and Ronco introduced the notion of a trioid as an algebra defined on a set with three binary associative operations. Every trialgebra is a linear analog of a trioid. Our paper is devoted to the study of verbal congruences on trioids. We characterize the least abelian dimonoid congruences, the least \(n\)-nilpotent dimonoid congruences, the least left (right) \(n\)-trinilpotent dimonoid congruence, the least \(n\)-nilpotent semigroup congruence and the least left (right) \(n\)-nilpotent semigroup congruence on the free trioid. The obtained results can be useful in trialgebra theory. |
|---|