On a Semigroup of Sets of Transformations with Restricted Range: Ananya Anantayasethi, Joerg Koppitz - Team, Support (Thai Journal of Mathematics, 2016)
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 ).