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    A partially ordered semigroup of Boolean spaces.

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    Author
    Hadida, Ahmed Mohamed.
    Issue Date
    1988
    Keywords
    Semigroups.
    Algebra, Boolean.
    Lattice theory.
    Advisor
    Pierce, Richard S.
    
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    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
    In this thesis we are concerned with arithmetic in a certain partially ordered, commutative semigroup D. The first chapter investigates the class of countable Boolean algebras from which this semigroup arises. The elements of D correspond to the isomorphism classes of the Boolean algebras under consideration. In Chapter 2 we begin the study of the semigroup structure of D. D is axiomatically described by three groups of axioms. It is proved that these axioms are categorical. The ordering of D is used to investigate the multiplication. The set of T of torsion elements of D (elements with only finite many distinct powers), form a subsemigroup whose structure is studied. There is a natural torsion free quotient D/T whose structure is also investigated. In Chapter 3, the axioms are used to characterize elements s of T in terms of the arithmetic in the subsemigroup generated by the elements that are smaller than s. The characterization is used to determine elements of T that cover a single element. In the last part of Chapter 3, we obtain some sufficient, purely combinatorial conditions for an element to have infinite order.
    Type
    text
    Dissertation-Reproduction (electronic)
    Degree Name
    Ph.D.
    Degree Level
    doctoral
    Degree Program
    Philosophy
    Graduate College
    Degree Grantor
    University of Arizona
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    Dissertations

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