A Note on Regularity of Certain Semigroups of Transformations Preserving a Reflexive and Transitive Relation
Keywords:Reflexive relation, Regular element, Transformation semigroup, Transitive relation
In this paper, we introduce semigroups of transformations that preserve a reflexive and transitive relation. These semigroups are generalizations of well-known classes of transformation semigroups, namely semigroups of transformations preserving an equivalence relation and semigroups of order-preserving transformations. Additionally, we investigate the necessary and sufficient conditions for elements within such a semigroup, in certain cases, to be regular. These results extend the existing knowledge in the aforementioned semigroups.
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