Regularity of Semigroups of Transformations Whose Characters Form the Semigroup of a Δ -Structure

Abstract

In this paper, we make use of the notion of the character of a transformation on a fixed set $X$ , provided by Purisang and Rakbud in 2016, and the notion of a $\mathrm{\Delta }$ -structure on $X$ , provided by Magill Jr. and Subbiah in 1974, to define a sub-semigroup of the full-transformation semigroup $T\left(X\right)$ . We also define a sub-semigroup of that semigroup. The regularity of those two semigroups is also studied.