# António Malheiro

## Associate Professor w/ habilitation, Mathematics Department

Faculdade de Ciências e Tecnologia UNL, Monte da Caparica, 2829-516 Caparica, Tel: (+351) 212948388 ext. 10832 (email)

Faculdade de Ciências e Tecnologia UNL, Monte da Caparica, 2829-516 Caparica, Tel: (+351) 212948388 ext. 10832 (email)

in

- Citation:
- Araújo, J., and A. Malheiro. "On finite complete presentations and exact decompositions of semigroups." Commun. Algebra. 39 (2011): 3866-3878.

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.

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