Zorn vector matrices over commutative rings and the loops arising from their construction
type: CreativeWork
description: 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.
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.
author: Wells, Andrew
language: en
date published: 2010-01-01
date modified: 2026-07-24T02:38:34Z
provider: Iowa State University
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: Iowa State University

PropertyValue
property ID: DOI
value: 10.31274/etd-180810-2824