Partial actions of inverse and weakly left e-ample semigroups

Victoria Gould, Christopher Hollings

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We introduce partial actions of weakly left E-ample semigroups, thus extending both the notion of partial actions of inverse semigroups and that of partial actions of monoids. Weakly left E-ample semigroups arise very naturally as subsemigroups of partial transformation semigroups which are closed under the unary operation alpha bar right arrow alpha(+), where alpha(+) is the identity map on the domain of alpha. We investigate the construction of 'actions' from such partial actions, making a connection with the FA-morphisins of Gomes. We observe that if the methods introduced in the monoid case by Megrelishvili and Schroder, and by the second author, are to be extended appropriately to the case of weakly left E-ample semigroups, then we must construct not global actions, but so-called incomplete actions. In particular, we show that a partial action of a weakly left E-ample semigroup is the restriction of an incomplete action. We specialize our approach to obtain corresponding results for inverse semigroups.

Original languageEnglish
Pages (from-to)355-377
Number of pages23
JournalJournal of the australian mathematical society
Issue number3
Publication statusPublished - Jun 2009


  • augmented action
  • expansion
  • incomplete action
  • inverse semigroup
  • partial action
  • premorphism
  • weakly left E-ample semigroup

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