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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.14216 |
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| _version_ | 1866911009107607552 |
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| author | Mazzotta, Marzia Pilitowska, Agata |
| author_facet | Mazzotta, Marzia Pilitowska, Agata |
| contents | A set-theoretic solution to the Pentagon Equation can be described as a \emph{pentagon} algebra $(S, \cdot, \ast)$ such that $(S, \cdot)$ is a semigroup and the operations $\cdot$ and $\ast$ are related by two additional equations. This paper aims to investigate associative pentagon algebras in which $(S, \ast)$ is also a semigroup. We introduce and describe two families of associative pentagon algebras which are strongly determined by the properties of the semigroup $(S,\ast)$. We present a complete characterization of such algebras using semigroup equations. We also provide constructions of such associative pentagon algebras and give several classes of examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_14216 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Associative Pentagon Algebras Mazzotta, Marzia Pilitowska, Agata Rings and Algebras A set-theoretic solution to the Pentagon Equation can be described as a \emph{pentagon} algebra $(S, \cdot, \ast)$ such that $(S, \cdot)$ is a semigroup and the operations $\cdot$ and $\ast$ are related by two additional equations. This paper aims to investigate associative pentagon algebras in which $(S, \ast)$ is also a semigroup. We introduce and describe two families of associative pentagon algebras which are strongly determined by the properties of the semigroup $(S,\ast)$. We present a complete characterization of such algebras using semigroup equations. We also provide constructions of such associative pentagon algebras and give several classes of examples. |
| title | Associative Pentagon Algebras |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2506.14216 |