Publicações > Artigos em Revistas Internacionais

The free ample monoid

Fountain, John; Gomes, Gracinda M. S.; Gould, Victoria

International Journal of Algebra and Computation , 19(4) (2009), 527-554

We show that the free weakly E-ample monoid on a set X is a full submonoid of the free inverse monoid FIM(X) on X. Consequently, it is ample, and so coincides with
both the free weakly ample and the free ample monoid FAM(X) on X. We introduce the notion of a semidirect product Y ∗ T of a monoid T acting doubly on a semilattice Y with identity. We argue that the free monoid X∗ acts doubly on the semilattice Y of
idempotents of FIM(X) and that FAM(X) is embedded in
Y * X*. Finally we show that every weakly E-ample monoid has a proper ample cover.