Domain theory, which studies directed complete partially ordered
sets, was introduced by Scott in the 1970's as a foundation for
programming semantics and provides an abstract model of
computation, and has grown into a respected field on the
borderline between mathematics and computer science.
In this paper, we consider actions of a semigroup (monoid or
group) on directed complete posets and study the algebraic notion
of retractness with respect to Scott closed embeddings and its
relation to direct sum in the categories so obtained.
