A nonfinitely based additively idempotent semiring of order four
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866917498915389440 |
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| author | Yue, Mengya Ren, Miaomiao |
| author_facet | Yue, Mengya Ren, Miaomiao |
| contents | We first establish a sufficient condition for an additively idempotent semiring to be nonfinitely based. As applications, we exhibit several examples of additively idempotent semirings satisfying this condition, including a $4$-element semiring $S_{(4,124)}$ whose additive reduct has two minimal elements and two coatoms. Consequently, these semirings have no finite basis for their identities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_15493 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A nonfinitely based additively idempotent semiring of order four Yue, Mengya Ren, Miaomiao Group Theory We first establish a sufficient condition for an additively idempotent semiring to be nonfinitely based. As applications, we exhibit several examples of additively idempotent semirings satisfying this condition, including a $4$-element semiring $S_{(4,124)}$ whose additive reduct has two minimal elements and two coatoms. Consequently, these semirings have no finite basis for their identities. |
| title | A nonfinitely based additively idempotent semiring of order four |
| topic | Group Theory |
| url | https://arxiv.org/abs/2605.15493 |