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On the varieties of ai-semirings satisfying \({x^{3}\approx x}\)

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The aim of this paper is to study the varieties of ai-semirings satisfying \({x^{3}\approx x}\) . It is shown that the collection of all such varieties forms a distributive lattice of order 179. Also, all of them are finitely based and finitely generated. This generalizes and extends the main results obtained by Ghosh et al., Pastijn and Ren and Zhao.

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Authors and Affiliations

  1. School of Mathematics, Northwest University, Xi’an, Shaanxi, 710127, P.R. China

    Miao Miao Ren, Xian Zhong Zhao & Ai Fa Wang

Authors
  1. Miao Miao Ren
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  2. Xian Zhong Zhao
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  3. Ai Fa Wang
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Corresponding author

Correspondence to Xian Zhong Zhao.

Additional information

Presented by M. Jackson.

The authors are supported by National Natural Science Foundation of China (11571278). The first author is supported by Scientific Research Foundation of Northwest University (15NW24) and Natural Science Foundation of Shannxi Province (2015JQ1210). The second author is supported by National Natural Science Foundation of China (11261021) and Grant of Natural Science Foundation of Jiangxi Province (20142BAB201002).

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Ren, M.M., Zhao, X.Z. & Wang, A.F. On the varieties of ai-semirings satisfying \({x^{3}\approx x}\) . Algebra Univers. 77, 395–408 (2017). https://doi.org/10.1007/s00012-017-0438-z

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  • DOI: https://doi.org/10.1007/s00012-017-0438-z

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