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...

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Збережено в:
Бібліографічні деталі
Дата:2024
Автор: Zhuchok, Anatolii V.
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
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Назва журналу:Algebra and Discrete Mathematics

Репозитарії

Algebra and Discrete Mathematics
Опис
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.