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A new approach to a network of congruences on an inverse semigroup

  • Ying-Ying Feng
  • Li-Min WangEmail author
  • Lu Zhang
  • Hai-Yuan Huang
Research Article

Abstract

This paper enriches the list of known properties of congruence sequences starting from the universal relation and successively performing the operators lower k and lower t. Two series of inverse semigroups, namely \(\ker {\alpha _n}\)-is-Clifford semigroups and \(\beta _n\)-is-over-E-unitary semigroups, are investigated. Two congruences, namely \(\alpha _{n+2}\) and \(\beta _{n+2}\), are found to be the least \(\ker {\alpha _n}\)-is-Clifford and least \(\beta _n\)-is-over-E-unitary congruences on S, respectively. A new system of implications is established for the quasivarieties of inverse semigroups induced by the min network.

Keywords

Inverse semigroup Congruence Ker \(\alpha _n\)-is-Clifford semigroup \(\beta _n\)-is-over-E-unitary semigroup Min network 

Notes

Acknowledgements

The authors are grateful to the careful referee for thoughtful comments and insights which helped to improve the paper, in particular, with regard to Lemma 2.4 and Proposition 2.17. The first author would like to thank Professor Victoria Gould for her continuing support and encouragement. This work is supported by a Grant of the National Natural Science Foundation of China (11871150) and a Grant of the Ministry of Education of China (18YJCZH206).

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Copyright information

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

Authors and Affiliations

  • Ying-Ying Feng
    • 1
  • Li-Min Wang
    • 2
    Email author
  • Lu Zhang
    • 2
  • Hai-Yuan Huang
    • 2
  1. 1.Department of MathematicsFoshan UniversityFoshanPeople’s Republic of China
  2. 2.School of MathematicsSouth China Normal UniversityGuangzhouPeople’s Republic of China

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