Skew Pairs of Idempotents in Partial Transformation Semigroups.

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. [ABSTRACT FROM AUTHOR]