A presentation for the dual symmetric inverse monoid

David Easdown, James East, D.G. FitzGerald

Abstract

The dual symmetric inverse monoid on an n-set is the inverse monoid of all isomorphisms between quotients of the set, where n is a nonnegative integer. We give a monoid presentation for it, and, along the way, establish criteria for a monoid to be inverse when it is generated by completely regular elements.

Keywords: dual symmetric inverse monoid.

AMS Subject Classification: Primary 20M18; secondary 20M05.