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Green’s relations and regularity for semigroups of transformations that preserve reverse direction equivalence

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Abstract

Let T X denote the full transformation semigroup on a set X. For an equivalence E on X, let

$$T_{\exists}(X)=\{\alpha\in T_X:\forall x,y\in X,(x\alpha,y\alpha)\in E\Rightarrow(x,y)\in E\}.$$

Then T ∃(X) is exactly the semigroup of mappings on the topological space X for which the collection of all E-classes is a basis. In this paper, we discuss regularity of elements and Green’s relations for T ∃(X).

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Authors and Affiliations

  1. School of Mathematics and Computer Science, Guizhou Normal University, Guiyang, 550001, China

    Lun-Zhi Deng & Tai-Jie You

  2. School of Mathematical Sciences, Xiamen University, Xiamen, 361005, China

    Lun-Zhi Deng & Ji-Wen Zeng

Authors
  1. Lun-Zhi Deng
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  2. Ji-Wen Zeng
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  3. Tai-Jie You
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Corresponding author

Correspondence to Lun-Zhi Deng.

Additional information

Communicated by Thomas E. Hall.

This work is supported by the Science and Technology Foundation of Guizhou Province, P.R. China (LKS [2010] 02).

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Deng, LZ., Zeng, JW. & You, TJ. Green’s relations and regularity for semigroups of transformations that preserve reverse direction equivalence. Semigroup Forum 83, 489–498 (2011). https://doi.org/10.1007/s00233-011-9344-4

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  • DOI: https://doi.org/10.1007/s00233-011-9344-4

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