  In 1996 Jespers and Wang classified finite semigroups whose integral
semigroup ring has finitely many units. In a recent paper, Iwaki-Juriaans-Souza
Filho continued this line of research by partially classifying the finite
semigroups whose rational semigroup algebra %over a field of characteristic
zero, contains a ${\mathbb{Z}}$-order with hyperbolic unit group. In this paper
we complete this classification by handling the case in which the semigroup is
semi-simple.
