Costa, José CarlosNogueira, ConceiçãoNogueira, Conceição2025-04-152025-04-152009-02Costa, José Carlos; Nogueira, Conceição (2009). Complete Reducibility of the Pseudovariety Ls1. International Journal of Algebra and Computation. https://doi.org/10.1142/s021819670900507x.0218-1967http://hdl.handle.net/10400.8/12802Palavras-chave: Semigroup; pseudovariety; pseudoword; system of equations; implicit signature; complete tameness; complete reducibility; local semillatice; infinite word.In this paper we prove that the pseudovariety LSl of local semilattices is completely κ-reducible, where κ is the implicit signature consisting of the multiplication and the ω-power. Informally speaking, given a finite equation system with rational constraints, the existence of a solution by pseudowords of the system over LSl implies the existence of a solution by κ-words of the system over LSl satisfying the same constraints.engSemigrouppseudovarietypseudowordsystem of equationsimplicit signaturecomplete tamenessjournal article10.1142/s021819670900507x1793-6500