Finite Semigroups Satisfying an Identity $x_1 \dots x_n \approx ρ(x_1, \dots, x_n)$
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912601673302016 |
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| author | Thumm, Alexander |
| author_facet | Thumm, Alexander |
| contents | We determine the maximal pseudovarieties of finite semigroups that satisfy an identity of the form $x_1 \dots x_n \approx ρ(x_1, \dots, x_n)$. Applying this classification, we further show that a pseudovariety of permutative semigroups satisfies a common permutation identity if and only if it satisfies an identity of the above form or, equivalently, if it does not contain $\mathbf{T} = [x^2 \approx xyx \approx 0]$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_19216 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Finite Semigroups Satisfying an Identity $x_1 \dots x_n \approx ρ(x_1, \dots, x_n)$ Thumm, Alexander Rings and Algebras 20M07 We determine the maximal pseudovarieties of finite semigroups that satisfy an identity of the form $x_1 \dots x_n \approx ρ(x_1, \dots, x_n)$. Applying this classification, we further show that a pseudovariety of permutative semigroups satisfies a common permutation identity if and only if it satisfies an identity of the above form or, equivalently, if it does not contain $\mathbf{T} = [x^2 \approx xyx \approx 0]$. |
| title | Finite Semigroups Satisfying an Identity $x_1 \dots x_n \approx ρ(x_1, \dots, x_n)$ |
| topic | Rings and Algebras 20M07 |
| url | https://arxiv.org/abs/2509.19216 |