Zorn vector matrices over commutative rings and the loops arising from their construction

dc.contributor.advisor Jonathan Smith
dc.contributor.author Wells, Andrew
dc.contributor.department Mathematics
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.copyright Fri Jan 01 00:00:00 UTC 2010
dc.date.embargo 2013-06-05
dc.date.issued 2010-01-01
dc.description.abstract <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>
dc.format.mimetype application/pdf
dc.identifier archive/lib.dr.iastate.edu/etd/11830/
dc.identifier.articleid 2900
dc.identifier.contextkey 2808098
dc.identifier.doi https://doi.org/10.31274/etd-180810-2824
dc.identifier.s3bucket isulib-bepress-aws-west
dc.identifier.submissionpath etd/11830
dc.identifier.uri https://dr.lib.iastate.edu/handle/20.500.12876/26036
dc.language.iso en
dc.source.bitstream archive/lib.dr.iastate.edu/etd/11830/Wells_iastate_0097E_11098.pdf|||Fri Jan 14 18:59:26 UTC 2022
dc.subject.disciplines Mathematics
dc.subject.keywords Moufang loop
dc.subject.keywords Paige loop
dc.subject.keywords quasigroup
dc.subject.keywords Vector matrix
dc.title Zorn vector matrices over commutative rings and the loops arising from their construction
dc.type article
dc.type.genre dissertation
dspace.entity.type Publication
relation.isOrgUnitOfPublication 82295b2b-0f85-4929-9659-075c93e82c48
thesis.degree.level dissertation
thesis.degree.name Doctor of Philosophy
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