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    A Theory And Development Of Quotient Rings

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    1970_LopachM_THS_0001243.pdf (7.847Mb)
    Author
    Lopach, Michael
    Advisor
    Alfred Murray; Noel Bowman
    Date of Issue
    1970-04-01
    Metadata
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    URI
    https://scholars.carroll.edu/handle/20.500.12647/3495
    Title
    A Theory And Development Of Quotient Rings
    Type
    thesis
    Abstract
    The purpose of this paper is a logical and clear development of the concept of quotient rings. The development will begin with the concept of groups and quotient groups, followed by discussions of rings, modular quotient rings, polynomial quotient rings, and, finally, an extension to the quotient field of rational numbers. The desired result is a unified presentation of some of the more fundamental ideas of modern abstract algebra, with a strong emphasis on the quotient ring and topics which are necessary for its development. However, rather than beginning immediately with the desired topic of rings, it will be much more advantageous to first of all define the symbols and terms which will be used throughout the work, and then to consider some of the simpler and more basic ideas which will make the main topic much easier to understand.
    Degree Awarded
    Bachelor's
    Semester
    Spring
    Department
    Mathematics, Engineering & Computer Science
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