Pei, Huisheng; Sun, Lei; Zhai, Hongcun Green’s relations for the variants of transformation semigroups preserving an equivalence relation. (English) Zbl 1127.20044 Commun. Algebra 35, No. 6, 1971-1986 (2007). The subject of this paper is \(T_E(X)\), the subsemigroup of the full transformation semigroup \(T_X\) of all mappings that respect a given equivalence relation \(E\) of \(X\). Fix \(\theta\) in \(T_E(X)\) and introduce a new semigroup operation \(\circ\) on \(T_E(X)\) by \(f\circ g=f\theta g\); this new semigroup is known as a variant semigroup of \(T_E(X)\). This paper calculates Green’s relations for variants and identifies the regular elements. Reviewer: Peter M. Higgins (Colchester) Cited in 13 Documents MSC: 20M20 Semigroups of transformations, relations, partitions, etc. Keywords:full transformation semigroups; Green relations; regular elements; variant semigroups; sandwich semigroups; congruences; equivalences PDFBibTeX XMLCite \textit{H. Pei} et al., Commun. Algebra 35, No. 6, 1971--1986 (2007; Zbl 1127.20044) Full Text: DOI References: [1] DOI: 10.1081/AGB-120029913 · Zbl 1068.20061 · doi:10.1081/AGB-120029913 [2] DOI: 10.1017/S0013091500004442 · Zbl 0525.20045 · doi:10.1017/S0013091500004442 [3] Howie J. M., Fundamentals of Semigroup Theory (1995) [4] DOI: 10.4153/CJM-1974-144-x · Zbl 0316.20041 · doi:10.4153/CJM-1974-144-x [5] DOI: 10.1112/plms/s3-31.2.194 · Zbl 0333.20051 · doi:10.1112/plms/s3-31.2.194 [6] DOI: 10.1017/S1446788700038933 · doi:10.1017/S1446788700038933 [7] Magill K. D., Czec. Math. J. 33 pp 221– (1983) [8] DOI: 10.1007/BF02573470 · Zbl 0804.20046 · doi:10.1007/BF02573470 [9] DOI: 10.1007/BF02574125 · Zbl 0852.20052 · doi:10.1007/BF02574125 [10] DOI: 10.1007/PL00005966 · Zbl 0912.20046 · doi:10.1007/PL00005966 [11] Pei H., East-West J. Math. 1 pp 197– (1999) [12] DOI: 10.1081/AGB-200040921 · Zbl 1072.20082 · doi:10.1081/AGB-200040921 [13] Pei H., J. Xinyang Teachers College 9 pp 106– (1996) [14] Pei H., J. Xinyang Teachers College 9 pp 217– (1996) [15] Pei H., Southeast Asian Bull. Math. 24 pp 73– (2000) [16] DOI: 10.1017/S1446788700023533 · Zbl 0329.20044 · doi:10.1017/S1446788700023533 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.