  In this paper we study endomorphism rings of finite global dimension over a
ring associated to a numerical semigroup. We construct these endomorphism rings
in two ways, called the lazy and greedy construction. The first main result of
this paper shows that the lazy construction enables us to obtain endomorphism
rings of arbitrarily large global dimension. The second main result of this
paper shows that the greedy construction gives us endomorphism rings which
always have global dimension two. As a consequence, for a fixed numerical
semigroup, the difference of the maximal possible value and the minimal
possible value of the global dimension of an endomorphism ring over that
numerical semigroup can be arbitrarily large.
