The flat semirings with nilpotent multiplicative reducts
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911513472663552 |
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| author | Gao, Zidong Ren, Miaomiao |
| author_facet | Gao, Zidong Ren, Miaomiao |
| contents | In this paper, we focus on the variety $\mathbf{NF}_3$ generated by all flat semirings with $3$-nilpotent multiplicative reducts. By introducing graph semirings, we characterize all subdirectly irreducible members of $\mathbf{NF}_3$. We prove that the variety $\mathbf{NF}_3$ has uncountably many subvarieties and show that every finitely generated subvariety of $\mathbf{NF}_3$ is a Cross variety. Moreover, we demonstrate that $\mathbf{NF}_3$ has a unique limit subvariety, which is generated by all acyclic graph semirings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_23047 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The flat semirings with nilpotent multiplicative reducts Gao, Zidong Ren, Miaomiao Group Theory In this paper, we focus on the variety $\mathbf{NF}_3$ generated by all flat semirings with $3$-nilpotent multiplicative reducts. By introducing graph semirings, we characterize all subdirectly irreducible members of $\mathbf{NF}_3$. We prove that the variety $\mathbf{NF}_3$ has uncountably many subvarieties and show that every finitely generated subvariety of $\mathbf{NF}_3$ is a Cross variety. Moreover, we demonstrate that $\mathbf{NF}_3$ has a unique limit subvariety, which is generated by all acyclic graph semirings. |
| title | The flat semirings with nilpotent multiplicative reducts |
| topic | Group Theory |
| url | https://arxiv.org/abs/2506.23047 |