Factoriality and the pin-reutenauer procedure

We consider implicit signatures over finite semigroups determined by sets of pseudonatural numbers. We prove that, under relatively simple hypotheses on a pseudovariety V of semigroups, the finitely generated free algebra for the largest such signature is closed under taking factors within the free pro-V semigroup on the same set of generators. Furthermore, we show that the natural analogue of the Pin-Reutenauer descriptive procedure for the closure of a rational language in the free group with respect to the profinite topology holds for the pseudovariety of all finite semigroups. As an application, we establish that a pseudovariety enjoys this property if and only if it is full.

A Responsabilidade Civil dos Gerentes e Administradores pelo pagamento das coimas e multas imputáveis à sociedade

Dissertação de mestrado em Direito dos Contratos e da Empresa

Development of composite auxetic structures for civil engineering applications

Tese de Doutoramento em Engenharia Têxtil