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...
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| Datum: | 2021 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Lugansk National Taras Shevchenko University
2021
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| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1732 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543245013614592 |
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| author | Zhuchok, A. V. |
| author_facet | Zhuchok, A. V. |
| author_sort | Zhuchok, A. V. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2021-04-11T06:11:31Z |
| description | 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. |
| first_indexed | 2025-12-02T15:30:31Z |
| format | Article |
| id | admjournalluguniveduua-article-1732 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:30:31Z |
| publishDate | 2021 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-17322021-04-11T06:11:31Z Structure of relatively free trioids Zhuchok, A. V. trioid, trialgebra, free trioid, free trialgebra, relatively free trioid, semigroup 08B20, 20M10, 20M50, 17A30, 17D9 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. Lugansk National Taras Shevchenko University 2021-04-10 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1732 10.12958/adm1732 Algebra and Discrete Mathematics; Vol 31, No 1 (2021) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1732/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/1732/791 Copyright (c) 2021 Algebra and Discrete Mathematics |
| spellingShingle | trioid trialgebra free trioid free trialgebra relatively free trioid semigroup 08B20 20M10 20M50 17A30 17D9 Zhuchok, A. V. Structure of relatively free trioids |
| title | Structure of relatively free trioids |
| title_full | Structure of relatively free trioids |
| title_fullStr | Structure of relatively free trioids |
| title_full_unstemmed | Structure of relatively free trioids |
| title_short | Structure of relatively free trioids |
| title_sort | structure of relatively free trioids |
| topic | trioid trialgebra free trioid free trialgebra relatively free trioid semigroup 08B20 20M10 20M50 17A30 17D9 |
| topic_facet | trioid trialgebra free trioid free trialgebra relatively free trioid semigroup 08B20 20M10 20M50 17A30 17D9 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1732 |
| work_keys_str_mv | AT zhuchokav structureofrelativelyfreetrioids |