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

Constructing Endomorphism Rings of Large Finite Global Dimension