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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.

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Algebraic and Combinatorial Properties of Schur Rings over Cyclic Groups

Misseldine, Andrew F. 01 May 2014 (has links)
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.
Schur ring
cyclic group
group ring
primitive idempotent
cyclotomic field
Wedderburn decomposition
representation theory
Galois theory
combinatorics
Mathematics

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