Mathematics (Dec 2021)

Skew Pairs of Idempotents in Partial Transformation Semigroups

  • Panuwat Luangchaisri,
  • Thawhat Changphas

DOI
https://doi.org/10.3390/math10010002
Journal volume & issue
Vol. 10, no. 1
p. 2

Abstract

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Let S be a regular semigroup. A pair (e,f) of idempotents of S is said to be a skew pair of idempotents if fe is idempotent, but ef 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.

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