Geodesic
A Note on the Abundance of Partial Transformation Semigroups with Fixed Point Sets
Discussiones Mathematicae. General Algebra and Applications, Tome 43 (2023) no. 2, pp. 241-247

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Given a non-empty set X and let P(X) be the partial transformation semigroup on X. For a fixed non-empty subset Y of X, let PFix(X,Y)={α∈ P(X):yα=y for all y ∈dom ( α ) ∩ Y}. Then PFix(X,Y) is a subsemigroup of P(X). In this paper, we show that PFix(X,Y) is always abundant, even if it is not regular. Moreover, unit regular and coregular elements of such semigroup are all completely characterized.
Keywords: partial transformation semigroup, abundance, unit regularity, coregularity 
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Wijarajak, Rattiya; Chaiya, Yanisa. A Note on the Abundance of Partial Transformation Semigroups with Fixed Point Sets. Discussiones Mathematicae. General Algebra and Applications, Tome 43 (2023) no. 2, pp. 241-247. http://geodesic.mathdoc.fr/item/DMGAA_2023_43_2_a5/