On the semigroups of partial one-to-one order-decreasing finite transformations

Abstract

Synopsis Let I n be the symmetric inverse semigroup on X n = {1,…, n} , let Sl n be the subsemigroup of strictly partial one-to-one self-maps of X n and let = { α ∊ SI n : x} ≦ x = U = ∅= be the semigroup of all partial one-to-one decreasing maps including the empty or zero map of X n . In this paper it is shown that is an (irregular, for n ≧ 2 ) type A semigroup with n D*-classes and D* = I*. Further, it is shown that is generated by the n(n + l )/2 quasi-idempotents in