A Note on Coregular Elements in Certain Semigroups of Transformations

Abstract

For a non-empty set X, let P(X) represent the partial transformation semigroup on X. For a non-empty subset Y of X, define as the semigroup . Then is a generalization of P(X) , encompassing all partial transformations on that maintain Y as an invariant set. This paper delves into exploring the characterization of coregular elements within and applies the results to obtain a similar characterization in relevant semigroups.