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_html":"<p>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</p> <p>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.</p>","abstract_has_math":false,"creators":["Wells, Andrew"],"institution":null,"degree_name":"Doctor of Philosophy","degree_level":"dissertation","degree_discipline":null,"degree_department":"Department of Mathematics","school":null,"contributors":[],"advisors":["Jonathan Smith"],"committee_chairs":[],"committee_members":[],"year":2010,"date_issued":"2010-01-01","date_published":"2010-01-01","updated_at":"2026-07-24T02:38:34Z","subjects":[],"languages":["en"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier.doi","label":"DOI","values":["https://doi.org/10.31274/etd-180810-2824"],"render_values":[{"text":"https://doi.org/10.31274/etd-180810-2824","href":"https://doi.org/10.31274/etd-180810-2824","code":true}]},{"key":"dc:identifier","label":"Identifier","values":["archive/lib.dr.iastate.edu/etd/11830/"],"render_values":[{"text":"archive/lib.dr.iastate.edu/etd/11830/","href":null,"code":true}]}]},"links":{"outbound_url":"https://dr.lib.iastate.edu/handle/20.500.12876/26036","outbound_label":"Repository record","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Jonathan Smith"]},{"key":"dc:contributor.department","label":"Department","values":["Department of Mathematics"]},{"key":"dc:creator","label":"Author","values":["Wells, Andrew"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2018-08-11T17:55:24.000"]},{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2020-06-30T02:38:29Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2020-06-30T02:38:29Z"]},{"key":"dc:date.issued","label":"Date","values":["2010-01-01"]},{"key":"dc:type","label":"Dc Type","values":["dissertation"]},{"key":"thesis:degree_level","label":"Degree Level","values":["dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["archive/lib.dr.iastate.edu/etd/11830/"]},{"key":"dc:identifier.doi","label":"DOI","values":["https://doi.org/10.31274/etd-180810-2824"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://dr.lib.iastate.edu/handle/20.500.12876/26036"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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.
"]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Zorn vector matrices over commutative rings and the loops arising from their construction"]}]}],"canonical_facts":{"dc:contributor.advisor":["Jonathan Smith"],"dc:contributor.department":["Department of Mathematics"],"dc:creator":["Wells, Andrew"],"dc:date":["2018-08-11T17:55:24.000"],"dc:date.accessioned":["2020-06-30T02:38:29Z"],"dc:date.available":["2020-06-30T02:38:29Z"],"dc:date.issued":["2010-01-01"],"dc:description.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.
"],"dc:format.mimetype":["application/pdf"],"dc:identifier":["archive/lib.dr.iastate.edu/etd/11830/"],"dc:identifier.doi":["https://doi.org/10.31274/etd-180810-2824"],"dc:identifier.uri":["https://dr.lib.iastate.edu/handle/20.500.12876/26036"],"dc:language.iso":["en"],"dc:title":["Zorn vector matrices over commutative rings and the loops arising from their construction"],"dc:type":["dissertation"],"thesis:degree_level":["dissertation"],"thesis:degree_name":["Doctor of Philosophy"]},"updated_at":"2026-07-24T02:38:34Z"}