The varieties of semilattice-ordered semigroups satisfying \(x^3\approx x\) and 详细信息    查看全文

• 作者：Miaomiao Ren ; Xianzhong Zhao
• 刊名：Periodica Mathematica Hungarica
• 出版年：2016
• 出版时间：June 2016
• 年：2016
• 卷：72
• 期：2
• 页码：158-170
• 全文大小：501 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Sciences
  Mathematics
  
• 出版者：Akad茅miai Kiad贸, co-published with Springer Science+Business Media B.V., Formerly Kluwer Academic
• ISSN：1588-2829
• 卷排序：72

文摘

The aim of this paper is to study the varieties of semilattice-ordered Burnside semigroups satisfying \(x^3\approx x\) and \(xy\approx yx.\) It is shown that the collection of all such varieties forms a distributive lattice of order 9. Also, all of them are finitely based and finitely generated. This gives a generalization and expansion of the results obtained by McKenzie and Romanowska (Contrib Gen Algebra Proc Klagenf Conf 1978 1:213–218, 1979).KeywordsSemilattice-ordered Burnside semigroupLatticeSubdirectly irreducible memberVariety0-Group