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| Título | Naturally ordered regular semigroups with an inverse monoid tranversal |
| Publication Type | Unpublished |
| Year of Publication | 2007 |
| Authors | Blyth TS, Santos AMH |
| Series Title | Preprint |
| 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 quasiideal. 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. |
| URL | http://www.dm.fct.unl.pt/sites/www.dm.fct.unl.pt/files/preprints/2007/9_07.pdf |