Abstract
In this note, we give a necessary and sufficient condition for elements of the naturally ordered transformation semigroup \(P_E(X)\) to be right compatible. This gives an answer to the problem raised by Pei and Deng (Commun Algebra 41(9):3308–3324, 2013).
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References
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Pei, H., Zhou, H.: Semigroups of partial transformations preserving an equivalence. Adv. Math. (in Chinese) 38(1), 103–116 (2009)
Pei, H., Deng, W.N.: Naturally ordered semigroups of partial transformations preserving an equivalence relation. Commun. Algebra 41(9), 3308–3324 (2013)
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The paper is supported by National Natural Science Foundation of China (No.11926415).
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Communicated by Mohammad Shahryari.
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Sun, L. A Note on Naturally Ordered Semigroups of Partial Transformations Preserving an Equivalence. Bull. Iran. Math. Soc. 47, 135–141 (2021). https://doi.org/10.1007/s41980-020-00371-z
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DOI: https://doi.org/10.1007/s41980-020-00371-z