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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| Datum: | 2024 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Lugansk National Taras Shevchenko University
2024
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| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2274 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543345711513600 |
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| author | Zhuchok, Anatolii V. |
| author_facet | Zhuchok, Anatolii V. |
| author_sort | Zhuchok, Anatolii V. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2024-06-27T08:42:43Z |
| description | 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. |
| first_indexed | 2026-02-08T08:01:45Z |
| format | Article |
| id | admjournalluguniveduua-article-2274 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2026-02-08T08:01:45Z |
| publishDate | 2024 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-22742024-06-27T08:42:43Z Certain verbal congruences on the free trioid Zhuchok, Anatolii V. trioid, free trioid, dimonoid, semigroup, congruence 08B20, 20M10, 20M50, 17A30, 17D99 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. Lugansk National Taras Shevchenko University 2024-06-27 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2274 10.12958/adm2274 Algebra and Discrete Mathematics; Vol 37, No 2 (2024) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2274/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/2274/1201 Copyright (c) 2024 Algebra and Discrete Mathematics |
| spellingShingle | trioid free trioid dimonoid semigroup congruence 08B20 20M10 20M50 17A30 17D99 Zhuchok, Anatolii V. Certain verbal congruences on the free trioid |
| title | Certain verbal congruences on the free trioid |
| title_full | Certain verbal congruences on the free trioid |
| title_fullStr | Certain verbal congruences on the free trioid |
| title_full_unstemmed | Certain verbal congruences on the free trioid |
| title_short | Certain verbal congruences on the free trioid |
| title_sort | certain verbal congruences on the free trioid |
| topic | trioid free trioid dimonoid semigroup congruence 08B20 20M10 20M50 17A30 17D99 |
| topic_facet | trioid free trioid dimonoid semigroup congruence 08B20 20M10 20M50 17A30 17D99 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2274 |
| work_keys_str_mv | AT zhuchokanatoliiv certainverbalcongruencesonthefreetrioid |