Algebra Commons^™

N-Cycle Splines Over Sexy Rings, Jacob Tilden Cummings

Senior Projects Spring 2020

In this project we abstract the work of previous bard students by introducing the concept of splines over non-integers, non-euclidean domains, and even non-PIDs. We focus on n-cycles for some natural number n. We show that the concept of flow up class bases exist in PID splines the same way they do in integer splines, remarking the complications and intricacies that arise when abstracting from the integers to PIDs. We also start from scratch by finding a flow up class basis for n-cycle splines over the real numbers adjoin two indeterminates, denoted R[x,y] which necessitate more original techniques.