Flores, Zachary J., authorPeterson, Christopher, advisorDuflot, Jeanne, committee memberCavalieri, Renzo, committee memberRoss, Kathryn, committee member2020-08-312020-08-312020https://hdl.handle.net/10217/211775In this dissertation, we aim to study finitely generated modules over several different Noetherian rings and from varying perspectives. This work is divided into four main parts: The first part is a study of algebraic K-theory for a certain class of local Noetherian rings; the second discusses extending well-known results on Lefschetz properties for graded complete intersection algebras to a class of graded finite length modules using geometric techniques; the third discusses the structure of various algebraic and geometric invariants attached to the finite length modules from the previous section; and lastly, we discuss the structure of annihilating ideals of classes of hyperplane arrangements in projective space.born digitaldoctoral dissertationsengCopyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright.algebraic K-theorycommutative algebraLefschetz propertiesapolar algebrasalgebraic geometryhyperplane arrangementsText