REGULARITY IN SEMIGROUPS OF TRANSFORMATIONS WITH INVARIANT SETS
W. Choomanee, Preeyanuch Honyam, Jintana Sanwong · International Journal of Pure and Apllied Mathematics · 2013
Let T (X) be the semigroup of all transformations on a set X.For a fixed nonempty subset Y of X, letThen S(X, Y ) is a semigroup of total transformations on X which leave a subset Y of X invariant.In this paper, we characterize left regular, right regular and intra-regular elements of S(X, Y ) and consider the relationships between these elements.Moreover, we count the number of left regular elements of S(X, Y ) when X is a finite set.