Abstract
Suppose that X is an infinite set with |X | ≥ q ≥ ℵ0 and I(X) is the symmetric inverse semigroup defined on X. In 1984, Levi and Wood determined a class of maximal subsemigroups MA (using certain subsets A of X) of the Baer‐Levi semigroup BL(q) = {α ∈ I(X): dom α = X and |X∖Xα| = q}. Later, in 1995, Hotzel showed that there are many other classes of maximal subsemigroups of BL(q), but these are far more complicated to describe. It is known that BL(q) is a subsemigroup of the partial Baer‐Levi semigroup PS(q) = {α ∈ I(X) : |X∖Xα| = q}. In this paper, we characterize all maximal subsemigroups of PS(q) when |X | > q, and we extend MA to obtain maximal subsemigroups of PS(q) when |X | = q.
Highlights
We characterize all maximal subsemigroups of P S q when |X| > q, and we extend MA to obtain maximal subsemigroups of P S q when |X| q
Suppose that X is a nonempty set, and let P X denote the semigroup under composition of all partial transformations of X i.e., all mappings α : A → B, where A, B ⊆ X
In 3 the authors showed that P S q, the partial Baer-Levi semigroup on X, does not have these properties but it is right reductive in the sense that for every α, β ∈ P S q, if αγ βγ for all γ ∈ P S q, α β
Summary
Suppose that X is a nonempty set, and let P X denote the semigroup under composition of all partial transformations of X i.e., all mappings α : A → B, where A, B ⊆ X. In 3 the authors showed that P S q , the partial Baer-Levi semigroup on X, does not have these properties but it is right reductive in the sense that for every α, β ∈ P S q , if αγ βγ for all γ ∈ P S q , α β. In 4 , the authors studied some properties of Mitsch’s natural partial order defined on a semigroup see 5, Theorem 3 and some other partial orders defined on P S q. They described compatibility and the existence of maximal and minimal elements.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
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 callMore From: International Journal of Mathematics and Mathematical Sciences
Disclaimer: 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.
