Irreducible Polyadic Semigroups Admitting the Adjunction of a Neutral Element
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911161772933120 |
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| author | Marichal, Jean-Luc Mathonet, Pierre Waldhauser, Tamás |
| author_facet | Marichal, Jean-Luc Mathonet, Pierre Waldhauser, Tamás |
| contents | It was claimed in [4] that for any integer $n\geqslant 2$, a neutral element can be adjoined to an $n$-ary semigroup if and only if the $n$-ary semigroup is reducible to a binary semigroup. We show that the `only if' direction of this statement is incorrect when $n$ is odd. Moreover, we offer a comprehensive characterization of the class of irreducible $n$-ary semigroups, for odd $n$, that admit the adjunction of a neutral element. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_14947 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Irreducible Polyadic Semigroups Admitting the Adjunction of a Neutral Element Marichal, Jean-Luc Mathonet, Pierre Waldhauser, Tamás Rings and Algebras Group Theory 16B99, 20M99, 20N15 It was claimed in [4] that for any integer $n\geqslant 2$, a neutral element can be adjoined to an $n$-ary semigroup if and only if the $n$-ary semigroup is reducible to a binary semigroup. We show that the `only if' direction of this statement is incorrect when $n$ is odd. Moreover, we offer a comprehensive characterization of the class of irreducible $n$-ary semigroups, for odd $n$, that admit the adjunction of a neutral element. |
| title | Irreducible Polyadic Semigroups Admitting the Adjunction of a Neutral Element |
| topic | Rings and Algebras Group Theory 16B99, 20M99, 20N15 |
| url | https://arxiv.org/abs/2509.14947 |