A Noncommutative Catenoid

Abstract: Noncommutative geometry generalizes many geometric results from such fields as differential geometry and algebraic geometry to a context where commutativity cannot be assumed. Unfortunately there are few concrete non-trivial examples of noncommutative objects. The aim of this thesis is to construct a noncommutative surface  which will be a generalization of the well known surface called the catenoid. This surface will be constructed using the Diamond lemma, derivations will be constructed over  and a general localization will be provided using the Ore condition.