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This article is cited in 4 scientific papers (total in 4 papers)
RESEARCH ARTICLE
Structure of relatively free trioids
A. V. Zhuchok Department of Algebra and System Analysis, Luhansk Taras Shevchenko National University, Gogol Square, 1, Starobilsk 92703, Ukraine
Abstract:
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.
Keywords:
trioid, trialgebra, free trioid, free trialgebra, relatively free trioid, semigroup.
Received: 30.11.2020
Citation:
A. V. Zhuchok, “Structure of relatively free trioids”, Algebra Discrete Math., 31:1 (2021), 152–166
Linking options:
https://www.mathnet.ru/eng/adm793 https://www.mathnet.ru/eng/adm/v31/i1/p152
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Abstract page: | 77 | Full-text PDF : | 37 | References: | 22 |
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