Naturally ordered regular semigroups with an inverse monoid transversal

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Abstract

The notion of an inverse transversal of a regular semigroup is well-known. Here we investigate naturally ordered regular semigroups that have an inverse transversal. Such semigroups are necessarily locally inverse and the inverse transversal is a quasi-ideal. After considering various general properties that relate the imposed order to the natural order, we highlight the situation in which the inverse transversal is a monoid. The regularity of Green’s relations is also characterised. Finally, we determine the structure of a naturally ordered regular semigroup with an inverse monoid transversal.
Original languageEnglish
Pages (from-to)71-86
Number of pages15
JournalSemigroup Forum
Volume76
Issue number1
DOIs
Publication statusPublished - 1 Jan 2008

Keywords

  • Inverse transversal
  • Regular semigroup
  • Natural order

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