A Note on Naturally Ordered Semigroups of Partial Transformations Preserving an Equivalence


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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    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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Correspondence to Lei Sun.

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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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  • Partial transformation semigroups
  • Natural partial order
  • Right compatibility

Mathematics Subject Classification

  • 20M20
  • 04A05