Semigroups of partial transformations with invariant set: Green's relations, unit regularity and directly finiteness
Jitsapa Srisawat, Yanisa Chaiya · Discussiones Mathematicae - General Algebra and Applications · 2024
Given a nonempty set X, and let P (X) denote the partial transformation semigroup on X.For a nonempty subset Y of X, define P T (X, Y ) as followsThen P T (X, Y ) is a generalization of P (X), consisting of all partial transformations on X that leave Y as an invariant set.In this paper, we investigate the Green's relations and explore all unit regular elements.Additionally, we determine the necessary and sufficient conditions for P T (X, Y ) to be unit regular and directly finite.