Sun, Lei A note on naturally ordered semigroups of partial transformations preserving an equivalence. (English) Zbl 1494.06009 Bull. Iran. Math. Soc. 47, No. 1, 135-141 (2021). 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)]. Cited in 2 Documents MSC: 06F05 Ordered semigroups and monoids 20M20 Semigroups of transformations, relations, partitions, etc. Keywords:partial transformation semigroups; natural partial order; right compatibility Citations:Zbl 1277.20075 PDFBibTeX XMLCite \textit{L. Sun}, Bull. Iran. Math. Soc. 47, No. 1, 135--141 (2021; Zbl 1494.06009) Full Text: DOI 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.