Regularity of Some Sandwich Semigroups of Transformations Defined by the Notion of Character

A. In this paper, we extend the notion of the character of a full transformation on a set, as introduced by Purisang and Rakbud in 2016, to the context of transformations, not necessarily full, from one set into another.Furthermore, we utilize this extended notion of character to define some sandwich semigroups of transformations and subsequently establish quotient semigroups derived from these sandwich semigroups.Additionally, we conduct a general study on the regularity of our quotient and sandwich semigroups of transformations.Finally, we apply our findings to determine the regularity of specific sandwich semigroups of transformations.