Comments on "Regularity of a Particular Subsemigroup of the Semigroup of Transformations Preserving an Equivalence"
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In this short note, we present some comments on the statement of Theorem 1.13 in a paper by Jittisak Rakbud [Regularity of a particular subsemigroup of the semigroup of transformations preserving an equivalence, Kyungpook Mathematical Journal, 58, 627–635, 2018]. In fact, we identify that the statement of Theorem 1.13 is flawed, and provide a counterexample to the statement of Theorem 1.13. Moreover, we give the correct statement of Theorem 1.13.
Abstract
In this short note, we present some comments on the statement of Theorem 1.13 in a paper by Jittisak Rakbud [Regularity of a particular subsemigroup of the semigroup of transformations preserving an equivalence, Kyungpook Mathematical Journal, 58, 627–635, 2018]. In fact, we identify that the statement of Theorem 1.13 is flawed, and provide a counterexample to the statement of Theorem 1.13. Moreover, we give the correct statement of Theorem 1.13.