Magnifiers in some semigroups of partial transformations [Articol]

Abstract

Let P(X) be the semigroup of all partial transformations on a set X. For a nonempty subset Y of X and a submonoid S(Y ) of P(Y ), denote by PS(Y )(X) the semigroup of all partial transformations f 2 P(X) such that the restriction fjY of f to Y belongs to S(Y ). We describe left and right magnifiers in PS(Y )(X). We apply these general results to describe magnifiers in PI(Y )(X), where I(Y ) is the symmetric inverse semigroup on Y . We identify corresponding known results on PP(Y )(X) and P (Y )(X), where (Y ) is the submonoid of P(Y ) consisting of all partial surjective transformations on Y .