Degree Type

Dissertation

Date of Award

2010

Degree Name

Doctor of Philosophy

Department

Mathematics

First Advisor

Jonathan Smith

Abstract

This thesis shows that the Zorn vector matrix construction which Paige used to construct simple nonassociative Moufang loops over finite fields can, in fact, be done over any commutative ring with the proper adjustments. The resulting loops are still Moufang, but no longer simple in general. Given a commutative ring and an ideal of that ring, the loop constructed over that ring can be decomposed into two pieces. In this way, it is shown that the loop

constructed over Z/4Z shares some structure with the Paige loop constructed over the finite field Z/2Z. An in depth study of the loop constructed over Z/4Z follows including significant portions of the subloop lattice and a variety of structural results.

Copyright Owner

Andrew Thomas Wells

Language

en

Date Available

2012-04-30

File Format

application/pdf

File Size

84 pages

Included in

Mathematics Commons

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