Structure of relatively free trioids

Loday and Ronco introduced the notions of a~trioid and a trialgebra, and constructed the free trioid of rank \(1\) and the free trialgebra. This paper is a survey of recent developments in the study of free objects in the varieties of trioids and trialgebras. We present the constructions of the free...

Повний опис

Збережено в:
Бібліографічні деталі
Дата:2021
Автор: Zhuchok, A. V.
Формат: Стаття
Мова:English
Опубліковано: Lugansk National Taras Shevchenko University 2021
Теми:
Онлайн доступ:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1732
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 notions of a~trioid and a trialgebra, and constructed the free trioid of rank \(1\) and the free trialgebra. This paper is a survey of recent developments in the study of free objects in the varieties of trioids and trialgebras. We present the constructions of the free trialgebra and the free trioid, the free commutative trioid, the free \(n\)-nilpotent trioid, the free left (right) \(n\)-trinilpotent trioid, and the free rectangular trioid. Some of these results can be applied to constructing relatively free trialgebras.