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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.16553 |
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| _version_ | 1866912843167694848 |
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| author | Ploščica, Miroslav Schwartzová, Radka Varga, Ivana |
| author_facet | Ploščica, Miroslav Schwartzová, Radka Varga, Ivana |
| contents | We investigate clones in the interval between the group polynomials and the ring polynomials of ${\mathbb Z}_8$. This is the simplest open case of the problem, as the answer is known for ${\mathbb Z}_{p^2}$ (with $p$ prime) and, in general, ${\mathbb Z}_n$ reduces to the case when $n$ is a prime power. The investigated structure proves to be very complicated, so we provide only a partial description. We restrict our attention to polynomials whose nonlinear monomials have even coefficients. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_16553 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Expansions of the group $Z_8$ (Part I) Ploščica, Miroslav Schwartzová, Radka Varga, Ivana Logic 08A40, 03B50 We investigate clones in the interval between the group polynomials and the ring polynomials of ${\mathbb Z}_8$. This is the simplest open case of the problem, as the answer is known for ${\mathbb Z}_{p^2}$ (with $p$ prime) and, in general, ${\mathbb Z}_n$ reduces to the case when $n$ is a prime power. The investigated structure proves to be very complicated, so we provide only a partial description. We restrict our attention to polynomials whose nonlinear monomials have even coefficients. |
| title | Expansions of the group $Z_8$ (Part I) |
| topic | Logic 08A40, 03B50 |
| url | https://arxiv.org/abs/2601.16553 |