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

<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>

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

dissertation

Department dc:contributor.department

Department of Mathematics

Year dc:date.issued

2010

Author dc:creator

• Wells, Andrew

Advisor dc:contributor.advisor

• Jonathan Smith

Language dc:language.iso

en

DOI

https://doi.org/10.31274/etd-180810-2824

Identifier

archive/lib.dr.iastate.edu/etd/11830/

OAI identifier oai:identifier

oai:dr.lib.iastate.edu:20.500.12876/26036