On a Semigroup of Sets of Transformations with Restricted Range

Ananya Anantayasethi, Joerg Koppitz

Abstract

This paper bases on the well-studied semigroup T(X; Y ) of all transfor-
mations on X with restricted range Y X. We introduce the semi-
group TP (X; Y ) of all non-empty subsets of T(X; Y ) under the operation
AB := fab : a 2 A;B 2 Bg. We determine the idempotent and regular ele-
ments in TP (X; Y ) for the case that jY j = 2. In particular, we characterize
the (maximal) regular subsemigroups of TP (X; Y ), the largest semiband,
and the (maximal) idempotent subsemigroups of TP (X; Y ).