Expansions of inverse semigroups

Mark V. Lawson, Stuart W. Margolis, Benjamin Steinberg

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


We construct the freest idempotent-pure expansion of an inverse semigroup, generalizing an expansion of Margolis and Meakin for the group case. We also generalize the Birget-Rhodes prefix expansion to inverse semigroups with an application to partial actions of inverse semigroups. In the process of generalizing the latter expansion, we are led to a new class of idempotent-pure homomorphisms which we term F-morphisms. These play the same role in the theory of idempotent-pure homomorphisms that F-inverse monoids play in the theory of É-unitary inverse semigroups.

Original languageEnglish
Pages (from-to)205-228
Number of pages24
JournalJournal of the Australian Mathematical Society
Issue number2
StatePublished - Apr 2006

Bibliographical note

Funding Information:
The second author was partially funded by the Excellency Center 'Group Theoretic Methods in the study of Algebraic Varieties' of the Israel Science foundation, INTAS grant 99-1224, Binational Science Foundation of Israel and the NSF. The third author was supported in part by NSF-NATO postdoctoral fellowship DGE-9972697, Praxis XXI scholarship BPD 16306 98, by Project SAPIENS 32817/99, by INTAS grant 99-1224, and by FCT through Centro de Matemdtica da Universidade do Porto. Much of this research took place at the Quasicrystals Workshop at the University of Essex funded by EPSRC grant number GR/M6544.


  • Birget-Rhodes expansion
  • Expansions
  • F-inverse semigroups
  • Inverse semigroups
  • Prehomomorphisms


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