Araújo, JoãoMalheiro, António2015-03-242015-03-242011Araújo, João; Malheiro, António - On finite complete presentations and exact decompositions of semigroups. "Communications in Algebra" [Em linha]. ISSN 0092-7872 (Print) 1532-4125 (Online). Vol. 39, nº 10 (2011), p. 1-120092-78721532-4125http://hdl.handle.net/10400.2/3807We 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.engjournal article10.1080/00927872.2010.514314