Abstract
We study a variety of Burnside ai-semirings satisfying \(x^n\approx x\). It is shown that the multiplicative semigroup of each member of such a variety is a regular orthocryptogroup. As an application, a model of the free object in such a variety is given. Also, some subvarieties of such a variety are characterized. Thus some results obtained respectively by Ghosh et al. (Order 22:109–128, 2005) and Pastijn and Zhao (Algebra Universalis 54:301–321, 2005) are generalized and extended.
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Acknowledgments
The authors are particularly grateful to Professor M. V. Volkov for his comments and suggestions contributed to this paper. The authors are supported by National Natural Science Foundation of China (11571278). The first author is supported by Scientific Research Program of Shaanxi Provincial Education Department (16JK1754) and Scientific Research Foundation of Northwest University (15NW24). The second author is supported by Grant of Natural Science Foundation of Jiangxi Province (20142BAB201002) and National Natural Science Foundation of China (11261021). The third author is supported by Natural Science Foundation of Shaanxi Province (2015JQ1210).
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Communicated by Mikhail Volkov.
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Ren, M., Zhao, X. & Shao, Y. On a variety of Burnside ai-semirings satisfying \(x^n\approx x\) . Semigroup Forum 93, 501–515 (2016). https://doi.org/10.1007/s00233-016-9819-4
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DOI: https://doi.org/10.1007/s00233-016-9819-4