On Maximal Subsemigroups of Partial Baer‐Levi Semigroups
Boorapa Singha, Jintana Sanwong · International Journal of Mathematics and Mathematical Sciences · 2011
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.