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 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.
Highlights
In [1], the authors defined a skew pair of idempotents in a regular semigroup as follows: Citation: Luangchaisri, P.; Changphas, T
Assume that P( X ) contains a discrete skew pair of Lemmas 4 and 5, it follows that | X | > 5
We considered the existence of skew pairs of idempotents on partial transformation semigroups using the cardinality of its based set
Summary
In [1], the authors defined a skew pair of idempotents in a regular semigroup as follows: Citation: Luangchaisri, P.; Changphas, T. We let x ∈ ran γ, there exists y ∈ dom γ such that γ(y) = x. P( X ) contains a strong skew pair of idempotents if and only if | X | ≥ 2.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
