SEMIGROUP OF INJECTIVE PARTIAL TRANSFORMATIONS WITH BOUNDED GAP AND FIXED DEFECT
Boorapa Singha · International Journal of Pure and Apllied Mathematics · 2013
Let X be an infinite set and suppose that ℵ 0 ≤ q ≤ |X|.In 2004, Pinto and Sullivan considered algebraic properties of P S(q), the partial Baer-Levi semigroup consisting of all injective partial transformations α of X such that |X \ Xα| = q.They also determined its subsemigroup S(q, r) = {α ∈ P S(q) : |X \ domα| ≤ r} where ℵ 0 ≤ r ≤ |X|.Recently, Singha and Sanwong showed that, when q < |X|, almost every maximal subsemigroup of P S(q) is induced by a maximal subsemigroup of S(q, r).Here, we use their work to describe some algebraic properties of S(q, r) including its Green's relation and its ideal structure.