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On free Burnside ai-semirings

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Abstract

In this paper we study the variety of the so-called Burnside ai-semirings. The notion of \((n, m)\)-closed subset of a semigroup is introduced and a model of a free Burnside ai-semiring is given by using the \((n, m)\)-closed subsets of a free Burnside semigroup. Thus some results obtained by Zhao, Kuřil and Polák are generalized and extended.

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Acknowledgments

The authors thank the referees for their help in the preparation of the final version of this paper. The authors also thank Dr. Yong Shao for discussions contributed to this paper. Miaomiao Ren is supported by China Postdoctoral Science Foundation (2011M501466). Xianzhong Zhao is supported by National Natural Science Foundation of China (11261021).

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Authors and Affiliations

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

    Miaomiao Ren

  2. College of Mathematics and Information Science, Jiangxi Normal University, Nanchang , 330022, Jiangxi, People’s Republic of China

    Xianzhong Zhao

Authors
  1. Miaomiao Ren
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  2. Xianzhong Zhao
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Correspondence to Xianzhong Zhao.

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Communicated by László Márki.

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Ren, M., Zhao, X. On free Burnside ai-semirings. Semigroup Forum 90, 174–183 (2015). https://doi.org/10.1007/s00233-014-9606-z

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  • DOI: https://doi.org/10.1007/s00233-014-9606-z

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