@article {zbMATH06000141, title = {On finite complete presentations and exact decompositions of semigroups.}, journal = {Commun. Algebra}, volume = {39}, number = {10}, year = {2011}, note = {

n/a

}, pages = {3866{\textendash}3878}, publisher = {Taylor \& Francis, Philadelphia, PA}, 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{\textendash}Sz{\'e}p 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.

}, issn = {0092-7872; 1532-4125/e}, doi = {10.1080/00927872.2010.514314}, url = {http://dx.doi.org/10.1080/00927872.2010.514314}, author = {J. Ara{\'u}jo and Malheiro, A.} }