Inverse Subsemigroups of the Monogenic Free Inverse Semigroup

Abstract

It is shown that every finitely generated inverse subsemigroup (submonoid) of the monogenic free inverse semigroup (monoid) is finitely presented. As a consequence, the homomorphism and the isomorphism problems for the monogenic free inverse semigroup (monoid) are proven to be decidable.

Keywords:

• Finitely presented
• Free inverse semigroup
• Homomorphism problem
• Isomorphism problem

2000 Mathematics Subject Classification:

• 20M05
• 20M18

ACKNOWLEDGMENT

The authors acknowledge support from F.C.T. through C.M.U.P. and the project POCTI/MAT/37670/2001, with funds from the programs POCTI and POSI, supported by national sources and the European Comunity fund FEDER.

Notes

Communicated by D. Easdown.