Inverting Elements in Rigid Monoids

Abstract

It is proved that the monoids between an archimedean, irreflexive and rigid monoid Mand its universal group G, obtained by adjoining inverses to M, are archimedean, irreflexive and rigid monoids.

Dedicated to the memory of Professor Ahmad Shamsuddin.

Key Words:

• Rigid monoid
• Archimedean monoid
• Irreflexive monoid
• 2-fir
• Monoid ring

Acknowledgment

The authors thank the referee for his or her comments and suggestions.

This work was partially supported by the DGICYT (Spain), through Grant PB98-0873, and by the Comissionat per Universitats i Recerca de la Generalitat de Catalunya(Grup de Recerca Consolidat 2001SGR00171).

Notes

Dedicated to the memory of Professor Ahmad Shamsuddin.