Naturally ordered regular semigroups with an inverse monoid transversal

T. S. Blyth, M. H. Almeida Santos

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


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 pages16
JournalSemigroup Forum
Publication statusPublished - Jan 2008


  • regular semigroup
  • natural order
  • inverse transversal


Dive into the research topics of 'Naturally ordered regular semigroups with an inverse monoid transversal'. Together they form a unique fingerprint.

Cite this