Persistent Link:
http://hdl.handle.net/10150/184369
Title:
A partially ordered semigroup of Boolean spaces.
Author:
Hadida, Ahmed Mohamed.
Issue Date:
1988
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)
Keywords:
Semigroups.; Algebra, Boolean.; Lattice theory.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Philosophy; Graduate College
Degree Grantor:
University of Arizona
Advisor:
Pierce, Richard S.

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titleA partially ordered semigroup of Boolean spaces.en_US
dc.creatorHadida, Ahmed Mohamed.en_US
dc.contributor.authorHadida, Ahmed Mohamed.en_US
dc.date.issued1988en_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.abstractIn 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.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectSemigroups.en_US
dc.subjectAlgebra, Boolean.en_US
dc.subjectLattice theory.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplinePhilosophyen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorPierce, Richard S.en_US
dc.contributor.committeememberGrove, Larryen_US
dc.contributor.committeememberStevenson, Fred W.en_US
dc.contributor.committeememberWood, Bruceen_US
dc.contributor.committeememberLomont, John S.en_US
dc.identifier.proquest8814239en_US
dc.identifier.oclc701244168en_US
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