In this dissertation, we explore the nature of Schur rings over finite cyclic groups, both algebraically and combinatorially. We provide a survey of many fundamental properties and constructions of Schur rings over arbitrary finite groups. After specializing to the case of cyclic groups, we provide an extensive treatment of the idempotents of Schur rings and a description for the complete set of primitive idempotents. We also use Galois theory to provide a classification theorem of Schur rings over cyclic groups similar to a theorem of Leung and Man and use this classification to provide a formula for the number of Schur rings over cyclic p-groups.
College and Department
Physical and Mathematical Sciences; Mathematics
BYU ScholarsArchive Citation
Misseldine, Andrew F., "Algebraic and Combinatorial Properties of Schur Rings over Cyclic Groups" (2014). Theses and Dissertations. 5259.
Schur ring, cyclic group, group ring, primitive idempotent, cyclotomic field, Wedderburn decomposition, representation theory, Galois theory, combinatorics