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The bands satisfying the strong isomorphism property

  • Baomin Yu
  • Xianzhong ZhaoEmail author
Research Article
  • 25 Downloads

Abstract

The power semigroup, or global, of a semigroup S is the set P(S) of all nonempty subsets of S equipped with the naturally defined multiplication. A class \({\mathcal {K}}\) of semigroups is globally determined if any two semigroups of \({\mathcal {K}}\) with isomorphic globals are themselves isomorphic. A class \({\mathcal {K}}\) of semigroups is said to satisfy the strong isomorphism property if for each pair \(S, T\in {\mathcal {K}}\) and each isomorphism \(\psi \) from P(S) onto P(T), \(\psi (\overline{S})=\overline{T}\), where \(\overline{S}=\{\{s\} \mid s\in S\}\subseteq P(S)\), \(\overline{T}=\{\{t\} \mid t\in T\} \subseteq P(T)\), and hence \(S\cong T\). In this paper we investigate classes of bands satisfying the strong isomorphism property. We provide a description of the largest subclass \({\overline{\mathcal {K}}}\) of \({\mathcal {K}}\) satisfying the strong isomorphism property for a globally determined class \({\mathcal {K}}\) of semigroups, and give some characterizations of the members of \({\overline{\mathcal {B}}}\) for class \({\mathcal {B}}\) of all bands.

Keywords

Band Power semigroup Global determinism The strong isomorphism property Characterization 

Notes

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of MathematicsNorthwest UniversityXi’anPeople’s Republic of China
  2. 2.School of Mathematics and PhysicsWeinan Normal UniversityWeinanPeople’s Republic of China

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