Abstract
We prove that given a finite (zero) exact right decomposition (M, T) of a semigroup S, if M is defined by a finite complete presentation, then S is also defined by a finite complete presentation. Exact right decompositions are natural generalizations to semigroups of coset decompositions in groups. As a consequence, we deduce that any Zappa–Szép extension of a monoid defined by a finite complete presentation, by a finite monoid, is also defined by such a presentation.
It is also proved that a semigroup M 0[A; I, J; P], where A and P satisfy some very general conditions, is also defined by a finite complete presentation.
2000 Mathematics Subject Classification:
ACKNOWLEDGEMENTS
We acknowledge with gratitude the suggestions made by both the referee and the editor, that strongly improved the article.
This work was developed within the project POCTI-ISFL-1-143 of CAUL, financed by FCT and FEDER. It is also part of the project “Semigroups and Languages – PTDC/MAT/69514/2006,” financed by FCT.
Notes
Communicated by M. Kambites.