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On the maximal subsemigroups of some transformation semigroups. (English) Zbl 1146.20045

Summary: Let \(\text{Sing}_n\) be the semigroup of all singular transformations on an \(n\)-element set. We consider two subsemigroups of \(\text{Sing}_n\): the semigroup \(O_n\) of all isotone singular transformations and the semigroup \(M_n\) of all monotone singular transformations. We describe the maximal subsemigroups of these two semigroups, and study the connections between them.

MSC:

20M20 Semigroups of transformations, relations, partitions, etc.
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[1] Garba G. U., Portugaliae Mathematica 51 pp 185–
[2] DOI: 10.1007/BF03025769 · Zbl 0769.20029 · doi:10.1007/BF03025769
[3] Clifford H., Amer. Math. Soc.
[4] DOI: 10.1007/s10114-004-0367-6 · Zbl 1061.20058 · doi:10.1007/s10114-004-0367-6
[5] Gyudzhenov Il., Comptes rendus de l’Academie bulgare des Sciences 59 pp 239–
[6] Gyudzhenov Il., Discussiones Mathematicae 26 pp 199–
[7] DOI: 10.1007/BF02194935 · Zbl 0359.20048 · doi:10.1007/BF02194935
[8] DOI: 10.1007/BF01848138 · Zbl 0477.20049 · doi:10.1007/BF01848138
[9] DOI: 10.1016/0021-8693(87)90223-7 · Zbl 0632.20011 · doi:10.1016/0021-8693(87)90223-7
[10] DOI: 10.1007/BF02195764 · Zbl 0379.20056 · doi:10.1007/BF02195764
[11] Bayramov P. A., Diskret Analiz 8 pp 3–
[12] DOI: 10.1007/s002330010117 · Zbl 0997.20057 · doi:10.1007/s002330010117
[13] You Taijie, Semigroup Forum 4 pp 243–
[14] Yang Xiuliang, Communications in Algebra 27 pp 4089– · Zbl 0943.20064 · doi:10.1080/00927879908826684
[15] Yang Xiuliang, Communications in Algebra 28 pp 1503– · Zbl 0948.20039 · doi:10.1080/00927870008826910
[16] DOI: 10.1081/AGB-100001675 · Zbl 0987.20046 · doi:10.1081/AGB-100001675
[17] Yang Xiuliang, Communications in Algebra 28 pp 3125– · Zbl 0952.20049 · doi:10.1080/00927870008827014
[18] DOI: 10.1007/s00233-005-0103-2 · Zbl 1101.20032 · doi:10.1007/s00233-005-0103-2
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