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Structure of relatively free trioids
Репозиторій DSpace/Manakin
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Structure of relatively free trioids
Інший ID:
DOI:10.12958/adm1732
2020 MSC: 08B20, 20M10, 20M50, 17A30, 17D99.
2020 MSC: 08B20, 20M10, 20M50, 17A30, 17D99.
Посилання:
Structure of relatively free trioids / A.V. Zhuchok // Algebra and Discrete Mathematics. — 2021. — Vol. 31, № 1. — С. 152–166. — Бібліогр.: 35 назв. — англ.
Підтримка:
Dedicated to the 60th anniversary of the Department of Algebra and Mathematical Logic of Taras Shevchenko National University of Kyiv
The author is supported by the National Research Foundation of Ukraine (grant no. 2020.02/0066).
Дата:
2021
Переглядів:
241
Завантажень:
127
Анотація:
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.
