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On the varieties generated by ai-semirings of order two

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Abstract

We study the variety \(\mathbf {S}_\mathbf{2}\) generated by all ai-semirings of order two. We prove that the lattice of all subvarieties of \(\mathbf {S}_{ \mathbf 2}\) is a Boolean algebra of order 64 and provide a finite equational basis for each member of the lattice.

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Acknowledgments

The authors are particularly grateful to Professors M. V. Volkov and X. Z. Zhao for their helpful comments and suggestions contributed to this paper. The authors also thank the anonymous referees for an unusually careful reading of the paper and posing a problem that has led to a substantial improvement of this paper. The first author is supported by China Postdoctoral Science Foundation (2011M501466) and a Grant of Natural Science Foundation of Shaanxi Province (2011JQ1017).

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Authors and Affiliations

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

    Yong Shao & Miaomiao Ren

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  1. Yong Shao
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  2. Miaomiao Ren
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Correspondence to Yong Shao.

Additional information

Communicated by Mikhail V. Volkov.

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Shao, Y., Ren, M. On the varieties generated by ai-semirings of order two. Semigroup Forum 91, 171–184 (2015). https://doi.org/10.1007/s00233-014-9667-z

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  • DOI: https://doi.org/10.1007/s00233-014-9667-z

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