We determine all isomorphisms between the endomorphism semigroups of free abelian dibands and prove that all automorphisms of the endomorphism semigroup of a free abelian diband are inner.

We extend the study of doppelsemigroups and introduce the notion of an ordered doppelsemigroup. We construct the ordered doppelsemigroup of binary relations on an arbitrary set and prove that every ordered doppelsemigroup ...