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 tri...
Saved in:
| Published in: | Algebra and Discrete Mathematics |
|---|---|
| Date: | 2021 |
| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Інститут прикладної математики і механіки НАН України
2021
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/188682 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Structure of relatively free trioids / A.V. Zhuchok // Algebra and Discrete Mathematics. — 2021. — Vol. 31, № 1. — С. 152–166. — Бібліогр.: 35 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862530115997532160 |
|---|---|
| author | Zhuchok, A.V. |
| author_facet | Zhuchok, A.V. |
| citation_txt | Structure of relatively free trioids / A.V. Zhuchok // Algebra and Discrete Mathematics. — 2021. — Vol. 31, № 1. — С. 152–166. — Бібліогр.: 35 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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 | 2025-11-24T03:02:05Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-188682 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-11-24T03:02:05Z |
| publishDate | 2021 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Zhuchok, A.V. 2023-03-11T13:31:29Z 2023-03-11T13:31:29Z 2021 Structure of relatively free trioids / A.V. Zhuchok // Algebra and Discrete Mathematics. — 2021. — Vol. 31, № 1. — С. 152–166. — Бібліогр.: 35 назв. — англ. 1726-3255 DOI:10.12958/adm1732 2020 MSC: 08B20, 20M10, 20M50, 17A30, 17D99. https://nasplib.isofts.kiev.ua/handle/123456789/188682 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. 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). en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Structure of relatively free trioids Article published earlier |
| spellingShingle | Structure of relatively free trioids Zhuchok, A.V. |
| 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/188682 |
| work_keys_str_mv | AT zhuchokav structureofrelativelyfreetrioids |