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Skew Pairs of Idempotents in Partial Transformation Semigroups

Author

Listed:
  • Panuwat Luangchaisri

    (Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand)

  • Thawhat Changphas

    (Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand)

Abstract

Let S be a regular semigroup. A pair ( e , f ) of idempotents of S is said to be a skew pair of idempotents if f e is idempotent, but e f is not. T. S. Blyth and M. H. Almeida (T. S. Blyth and M. H. Almeida, skew pair of idempotents in transformation semigroups, Acta Math. Sin. (English Series), 22 (2006), 1705–1714) gave a characterization of four types of skew pairs—those that are strong, left regular, right regular, and discrete—existing in a full transformation semigroup T ( X ) . In this paper, we do in this line for partial transformation semigroups.

Suggested Citation

  • Panuwat Luangchaisri & Thawhat Changphas, 2021. "Skew Pairs of Idempotents in Partial Transformation Semigroups," Mathematics, MDPI, vol. 10(1), pages 1-8, December.
    • Handle: RePEc:gam:jmathe:v:10:y:2021:i:1:p:2-:d:707206
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