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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2602.06972 |
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| _version_ | 1866914311633371136 |
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| author | Jiao, Jun Ren, Miaomiao |
| author_facet | Jiao, Jun Ren, Miaomiao |
| contents | We provide a complete classification of matrix semirings $\mathbf{M}_n(S)$ over two-element additively idempotent semirings $S$ with respect to the finite basis property.Our main theorem shows that for every integer $n \geq 2$,the semiring $\mathbf{M}_n(S)$ is finitely based if and only if $S$ is distinct from a distributive lattice. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_06972 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The finite basis problem for matrix semirings over a two-element additively idempotent semiring Jiao, Jun Ren, Miaomiao Rings and Algebras Group Theory We provide a complete classification of matrix semirings $\mathbf{M}_n(S)$ over two-element additively idempotent semirings $S$ with respect to the finite basis property.Our main theorem shows that for every integer $n \geq 2$,the semiring $\mathbf{M}_n(S)$ is finitely based if and only if $S$ is distinct from a distributive lattice. |
| title | The finite basis problem for matrix semirings over a two-element additively idempotent semiring |
| topic | Rings and Algebras Group Theory |
| url | https://arxiv.org/abs/2602.06972 |