REGULARITY FOR SEMIGROUPS OF TRANSFORMATIONS THAT PRESERVE EQUIVALENCE
For a semigroup S, an element aof Sis said to be regular if for some left (right) regular if for some and completely regular if and for some In this paper, we give a necessary and suffcient condition when elements of the transformation semigroup preserving equivalence to be regular, left regular, right regular and completely regular.
regular, left regular, right regular, completely regular.