Cross-connection structure of locally inverse semigroups

P. A. Azeef Muhammed, M. V. Volkov, K. Auinger

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

Locally inverse semigroups are regular semigroups whose idempotents form pseudo-semilattices. We characterize the categories that correspond to locally inverse semigroups in the realm of Nambooripad's cross-connection theory. Further, we specialize our cross-connection description of locally inverse semigroups to inverse semigroups and completely 0-simple semigroups, obtaining structure theorems for these classes. In particular, we show that the structure theorem for inverse semigroups can be obtained using only one category, quite analogous to the Ehresmann-Schein-Nambooripad Theorem; for completely 0-simple semigroups, we show that cross-connections coincide with structure matrices, thus recovering the Rees Theorem by categorical tools.
Original languageEnglish
Pages (from-to)123-159
Number of pages37
JournalInternational Journal of Algebra and Computation
Volume33
Issue number1
DOIs
Publication statusPublished - 1 Feb 2023

Bibliographical note

Publisher Copyright:
© 2023 World Scientific Publishing Company.

Keywords

  • Rees theorem
  • cross-connection
  • Ehresmann-Schein-Nambooripad theorem
  • inverse semigroup
  • completely 0 -simple semigroup
  • category
  • Locally inverse semigroup

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