• Login
    View Item 
    •   Home
    • UA Graduate and Undergraduate Research
    • UA Theses and Dissertations
    • Dissertations
    • View Item
    •   Home
    • UA Graduate and Undergraduate Research
    • UA Theses and Dissertations
    • Dissertations
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Browse

    All of UA Campus RepositoryCommunitiesTitleAuthorsIssue DateSubmit DateSubjectsPublisherJournalThis CollectionTitleAuthorsIssue DateSubmit DateSubjectsPublisherJournal

    My Account

    LoginRegister

    About

    AboutUA Faculty PublicationsUA DissertationsUA Master's ThesesUA Honors ThesesUA PressUA YearbooksUA CatalogsUA Libraries

    Statistics

    Most Popular ItemsStatistics by CountryMost Popular Authors

    Structures of circular planar nearrings

    • CSV
    • RefMan
    • EndNote
    • BibTex
    • RefWorks
    Thumbnail
    Name:
    azu_td_9234881_sip1_m.pdf
    Size:
    5.066Mb
    Format:
    PDF
    Description:
    azu_td_9234881_sip1_m.pdf
    Download
    Author
    Ke, Wen-Fong
    Issue Date
    1992
    Keywords
    Rings (Algebra)
    Near-rings.
    Advisor
    Clay, James R.
    
    Metadata
    Show full item record
    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
    The family of planar nearrings enjoys quite a few geometric and combinatoric properties. Circular planar nearrings are members of this family which have the character of circles of the complex plane. On the other hand, they also have some properties which one may not find among the circles of the complex plane. In this dissertation, we first review the definition and characterization of a planar nearring, and some various ways of constructing planar nearrings, as well as various ways of constructing BIBD's from a planar nearring. Circularity of a planar nearring is then introduced, and examples of circularity planar nearrings are given. Then, some nonisomorphic BIBD's arising from the same additive group of a planar nearring are examined. To provide examples of nonabelian planar nearrings, the structures of Frobenius groups with kernel of order 64 are completely determined and described. On the other hand, examples of Ferrero pairs (N, Φ)'s with nonabelian Φ, which produce circular planar nearrings, are provided. Finally, we study the structures of circular planar nearrings generated from the finite prime fields from geometric and combinatoric points of view. This study is then carried back to the complex plane. In turn, it gives a good reason for calling a block from a circular planar nearring a "circle."
    Type
    text
    Dissertation-Reproduction (electronic)
    Degree Name
    Ph.D.
    Degree Level
    doctoral
    Degree Program
    Mathematics
    Graduate College
    Degree Grantor
    University of Arizona
    Collections
    Dissertations

    entitlement

     
    The University of Arizona Libraries | 1510 E. University Blvd. | Tucson, AZ 85721-0055
    Tel 520-621-6442 | repository@u.library.arizona.edu
    DSpace software copyright © 2002-2017  DuraSpace
    Quick Guide | Contact Us | Send Feedback
    Open Repository is a service operated by 
    Atmire NV
     

    Export search results

    The export option will allow you to export the current search results of the entered query to a file. Different formats are available for download. To export the items, click on the button corresponding with the preferred download format.

    By default, clicking on the export buttons will result in a download of the allowed maximum amount of items.

    To select a subset of the search results, click "Selective Export" button and make a selection of the items you want to export. The amount of items that can be exported at once is similarly restricted as the full export.

    After making a selection, click one of the export format buttons. The amount of items that will be exported is indicated in the bubble next to export format.