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Regularity and Green's Relations on a Semigroup of Transformations with Restricted Range

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  • Jintana Sanwong
  • Worachead Sommanee

Abstract

Let be the full transformation semigroup on the set and let . Then is a sub-semigroup of determined by a nonempty subset of . In this paper, we give a necessary and sufficient condition for to be regular. In the case that is not regular, the largest regular sub-semigroup is obtained and this sub-semigroup is shown to determine the Green's relations on . Also, a class of maximal inverse sub-semigroups of is obtained.

Suggested Citation

  • Jintana Sanwong & Worachead Sommanee, 2008. "Regularity and Green's Relations on a Semigroup of Transformations with Restricted Range," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2008, pages 1-11, November.
    • Handle: RePEc:hin:jijmms:794013
    DOI: 10.1155/2008/794013
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    Cited by:

    1. Chollawat Pookpienlert & Preeyanuch Honyam & Jintana Sanwong, 2018. "Green’s Relations on a Semigroup of Transformations with Restricted Range that Preserves an Equivalence Relation and a Cross-Section," Mathematics, MDPI, vol. 6(8), pages 1-12, August.
    2. Worachead Sommanee, 2018. "The Regular Part of a Semigroup of Full Transformations with Restricted Range: Maximal Inverse Subsemigroups and Maximal Regular Subsemigroups of Its Ideals," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2018, pages 1-9, May.
    3. Kitsanachai Sripon & Ekkachai Laysirikul & Worachead Sommanee, 2023. "Left (Right) Regular Elements of Some Transformation Semigroups," Mathematics, MDPI, vol. 11(10), pages 1-12, May.

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