JournalspmVol. 64 / No. 4DOI 10.4171/pm/1792

Complete reducibility of systems of equations with respect to R

  • Jorge Almeida

    Faculdade de Ciências, Universidade do Porto, Portugal
  • José Carlos Costa

    Universidade Do Minho, Braga, Portugal
  • Marc Zeitoun

    Université de Bordeaux I, Talence, France
Complete reducibility of systems of equations with respect to R cover

You need to subscribe to download the article.

Abstract

It is shown that the pseudovariety {\sf R} of all finite {\mathcal R}-trivial semigroups is completely reducible with respect to the canonical signature. Informally, if the variables in a finite system of equations with rational constraints may be evaluated by pseudowords so that each value belongs to the closure of the corresponding rational constraint and the system is verified in {\sf R}, then there is some such evaluation which is ``regular'', that is one in which, additionally, the pseudowords only involve multiplications and -powers.