JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2020, Vol. 55 ›› Issue (12): 19-24.doi: 10.6040/j.issn.1671-9352.0.2020.319

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Maximal subsemigroups and the maximal regular subsemigroups of the semigroup H *(n,m)(r)

YUAN Yue, ZHAO Ping*   

  1. School of Mathematics Science, Guizhou Normal University, Guiyang 550025, Guizhou, China
  • Published:2020-12-01

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Abstract: Let Tn be the full transformation semigroup on Xn={1,2,…,n}. For any 1≤m≤n-1, let Xm={1,2,…,m}. Through the subsemigroupsG(n,m)={α∈T(n,m):(Xn\Xm)α=Xn\Xm}andH(n,m)={α∈T(n,m):(Xn\Xm)α⊆Xn\Xm}of the semigroup T(n,m)={α∈Tn:Xmα=Xm}, the subsemigroups of the semigroup H *(n,m)(r)={α∈H(n,m):|im(α)|≤r}∪G(n,m) are studied for 1≤m1, and it is proved that the maximal subsemigroups of H *(n,m)(r)are the same as the maximal regular subsemigroups.

Key words: full transformation semigroup, symmetric group, equivalence relation, maximal regular subsemigroup, maximal subsemigroup

CLC Number: 

  • O152.7
[1] YANG Xiuliang. Maximal semigroups of the finite singular transformation semigroup[J]. Communications in Algebra, 2001, 29(3):1175-1182.
[2] YOU Taijie. Maximal regular subsemigroups of certain semigroups of transformations[J]. Semigroup Forum, 2002, 64(3):391-396.
[3] YOU Taijie, YANG Xiuliang. A classification of the maximal idempotent generated subsemigroups of finite singular semigroups[J]. Semigroup Forum, 2002, 64(2):236-242.
[4] YANG Haobo, YANG Xiuliang. Maximal subsemigroups of finite transformation semigroups K(n,r)[J]. Acta Mathematica Sinica, 2004, 20(3):475-482.
[5] YANG Xiuliang, YANG Haobo. Maximal regular subsemibands of Singn[J]. Semigroup Forum, 2006, 72(1):75-93.
[6] ZHAO Ping, XU Bo, YANG Mei. Locally maximal idempotent-generated subsemigroups of singular orientation-preserving transformation semigroups[J]. Semigroup Forum, 2008, 77(2):187-195.
[7] ZHAO Ping. A classification of maximal idempotent-generated subsemigroups of singular orientation-preserving transformation semigroups[J]. Semigroup Forum, 2009, 79(2):377-384.
[8] ZHAO Ping. Maximal regular subsemibands of SOPn[J]. Semigroup Forum, 2010, 80(3):477-483.
[9] ZHAO Ping, HU Huabi, YOU Taijie. A note on maximal regular subsemigroups of the finite transformation semigroups T(n,r)[J]. Semigroup Forum, 2014, 88(2):324-332.
[10] ZHAO Ping, HU Huabi. Locally maximal regular subsemibands of the finite transformation semigroups T(n,r)[J]. Semigroup Forum, 2019, 98(1):172-183.
[11] TOKER K, AYIK H. On the rank of transformation semigroup T(n,m)[J]. Turk J Math, 2018, 42(4):1970-1977.
[12] HARDY G H, WRIGHT E M. An introduction to the theory of numbers[M]. 5th ed. Oxford University Press, 1979.
[13] HOWIE J M, MCEFADDEN R B. Idempotent rank in finite full transformation semigroups[J]. Proceedings of the Royal Society of Edinburgh, 1990, 114(3/4):161-167.
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