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The additively idempotent semiring \(S_7^0\) is nonfinitely based

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Abstract

We show that the additively idempotent semiring \(S_7^0\) has no finite basis for its equational theory. This answers an open problem posed by Jackson et al. (J Algebra 611:211–245, 2022).

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Acknowledgements

The authors are particularly grateful to Prof. Marcel Jackson for his valuable suggestions contributed to this paper. The authors also thank the anonymous referee for her/his valuable comments, suggestions and an unusually careful reading of the paper that have led to a substantial improvement of this paper.

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Authors and Affiliations

  1. School of Mathematics, Northwest University, Xi’an, 710127, Shaanxi, People’s Republic of China

    Yanan Wu, Miaomiao Ren & Xianzhong Zhao

Authors
  1. Yanan Wu
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  2. Miaomiao Ren
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  3. Xianzhong Zhao
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Correspondence to Miaomiao Ren.

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Communicated by Marcel Jackson.

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Miaomiao Ren is supported by National Natural Science Foundation of China (12371024) and Natural Science Foundation of Shaanxi Province (2022JM-009). Xianzhong Zhao is supported by National Natural Science Foundation of China (11971383).

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Wu, Y., Ren, M. & Zhao, X. The additively idempotent semiring \(S_7^0\) is nonfinitely based. Semigroup Forum (2024). https://doi.org/10.1007/s00233-024-10420-2

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