UC San Diego

Finding suitable methods for associating geometry to noncommutative graded algebras has been a goal for noncommutative algebraists for the last 20 years. While one method is to study the relationship between an algebra and its associated noncommutative category Proj, another method is to examine an algebra's corresponding point modules. This dissertation describes the point modules associated to some noncommutative graded algebras of dimension 3, where the graded pieces have the same dimensions as the graded pieces of a polynomial ring. These algebras have an infinite set of point modules and are regular if and only if they are domains