On a variety of Burnside ai-semirings satisfying \(x^n\approx x\)

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• 作者：Miaomiao Ren ; Xianzhong Zhao ; Yong Shao
• 关键词：Burnside ai ; semiring ; Congruence ; Green’s relation ; Regular orthocryptogroup ; Variety
• 刊名：Semigroup Forum
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：93
• 期：3
• 页码：501-515
• 全文大小：421 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Algebra
  
• 出版者：Springer New York
• ISSN：1432-2137
• 卷排序：93

文摘

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.