The finite basis problem for the endomorphism semirings of finite semilattices
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908872721039360 |
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| author | Dolinka, Igor Gusev, Sergey V. Volkov, Mikhail V. |
| author_facet | Dolinka, Igor Gusev, Sergey V. Volkov, Mikhail V. |
| contents | For every semilattice $\mathcal{A}=(A,+)$, the set $\mathrm{End}(\mathcal{A})$ of its endomorphisms forms a semiring under pointwise addition and composition. We prove that that if $\mathcal{A}$ is finite, then the endomorphism semiring $\mathrm{End}(\mathcal{A})$ has a finite identity basis if and only if $|A|\le 2$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_01212 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The finite basis problem for the endomorphism semirings of finite semilattices Dolinka, Igor Gusev, Sergey V. Volkov, Mikhail V. Rings and Algebras 16Y60, 08B05 For every semilattice $\mathcal{A}=(A,+)$, the set $\mathrm{End}(\mathcal{A})$ of its endomorphisms forms a semiring under pointwise addition and composition. We prove that that if $\mathcal{A}$ is finite, then the endomorphism semiring $\mathrm{End}(\mathcal{A})$ has a finite identity basis if and only if $|A|\le 2$. |
| title | The finite basis problem for the endomorphism semirings of finite semilattices |
| topic | Rings and Algebras 16Y60, 08B05 |
| url | https://arxiv.org/abs/2508.01212 |