Generalized Green'S Equivalences on the Subsemigroups of the Bicyclic Monoid

Abstract

We study generalized Green's equivalences on all subsemigroups of the bicyclic monoid B and determine the abundant (and adequate) subsemigroups of B.

Key Words:

• Bicyclic
• Green
• Semigroup
• Subsemigroup

2000 Mathematics Subject Classification:

• 20M10

ACKNOWLEDGMENTS

The first author acknowledges the support of the Fundaço para a Cincia e a Tecnologia (Portugal) through Unidade de Investigaço Matemática e Aplicaçes of the University of Aveiro and also the support of the project PTDC/MAT/65481/2006, which is partly funded by the European Community Fund FEDER.

Notes

Communicated by V. Gould.