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A note on naturally ordered semigroups of partial transformations preserving an equivalence. (English) Zbl 1494.06009

Summary: 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 H. Pei and W. Deng [Commun. Algebra 41, No. 9, 3308–3324 (2013; Zbl 1277.20075)].

MSC:

06F05 Ordered semigroups and monoids
20M20 Semigroups of transformations, relations, partitions, etc.

Citations:

Zbl 1277.20075
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References:

[1] Mitsch, H., A natural partial order for semigroups, Proc. Am. Math. Soc., 97, 3, 384-388 (1986) · Zbl 0596.06015
[2] Pei, H.; Zhou, H., Semigroups of partial transformations preserving an equivalence, Adv. Math. (in Chinese), 38, 1, 103-116 (2009)
[3] Pei, H.; Deng, WN, Naturally ordered semigroups of partial transformations preserving an equivalence relation, Commun. Algebra, 41, 9, 3308-3324 (2013) · Zbl 1277.20075
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