Persistent Link:
http://hdl.handle.net/10150/186931
Title:
Homomorphisms of planar nearrings.
Author:
Olson, Steven Jon.
Issue Date:
1994
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
This dissertation is about two types of nearring: the planar nearring and the partite nearring. The planar nearring is best known for its connection with block designs and the partite nearring is a generalization of the planar nearring which is useful to have when studying homomorphisms. After defining and describing partite nearrings we look at ideals and homomorphisms. We see that homomorphisms defined on partite nearrings always have "associated homomorphisms." We also look at several theorems that tell us when a function defined on a partite nearring is a nearring homomorphism. In the final section we look at a particular type of "vector-space-generated" planar nearring and describe the group of automorphisms on that nearring.
Type:
text; Dissertation-Reproduction (electronic)
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Mathematics; Graduate College
Degree Grantor:
University of Arizona
Committee Chair:
Clay, James R.

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titleHomomorphisms of planar nearrings.en_US
dc.creatorOlson, Steven Jon.en_US
dc.contributor.authorOlson, Steven Jon.en_US
dc.date.issued1994en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractThis dissertation is about two types of nearring: the planar nearring and the partite nearring. The planar nearring is best known for its connection with block designs and the partite nearring is a generalization of the planar nearring which is useful to have when studying homomorphisms. After defining and describing partite nearrings we look at ideals and homomorphisms. We see that homomorphisms defined on partite nearrings always have "associated homomorphisms." We also look at several theorems that tell us when a function defined on a partite nearring is a nearring homomorphism. In the final section we look at a particular type of "vector-space-generated" planar nearring and describe the group of automorphisms on that nearring.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineMathematicsen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.chairClay, James R.en_US
dc.contributor.committeememberBrillhart, Johnen_US
dc.contributor.committeememberMay, Warrenen_US
dc.identifier.proquest9517545en_US
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