Tolerance relations on eventually regular semigroups

A semigroup is called eventually regular if a power of each element is regular. Regular and group-bound semigroups are each eventually regular. A tolerance relation on an eventually regular semigroup is introduced, and Lallement's result for regular semigroups is generalized to eventually regular semigroups. Weakly compatible tolerances on semigroups are studied. This research was partially supported by the National Science Foundation of Qufu Normal University. The author wishes to thank T. E. Hall for his comments and help in preparing this paper for publication.