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dc.contributor.advisorMilovich, David K.
dc.creatorMontemayor, Rene
dc.date.accessioned2017-04-28T14:46:26Z
dc.date.available2017-04-28T14:46:26Z
dc.date.created2016-12
dc.date.submittedDecember 2016
dc.identifier.urihttp://hdl.handle.net/2152.4/97
dc.description.abstractHeindorf and Shapiro studied commuting pairs of Boolean subalgebras and showed that Boolean subalgebra pairs that commute retain their commutativity property after taking the exponential functor. Recently Milovich introduced the concept of commuting n-tuples and weakly commuting n-tuples of Boolean subalgebras. In particular, Milovich non-constructively proved that there exists a case where by applying the exponential functor to a triple, of finite Boolean subalgebras, the weakly commuting property is destroyed. The purpose of this paper is to find explicit examples of triples of finite subalgebras that weakly commute but when the exponential functor is applied, the weak commutativity property of this triple is destroyed. Using Python, a high level programming language, it was determined that the four atom finite Boolean Algebra has a triple of subalgebras whose weakly commuting property is destroyed when the exponential functor is applied. Furthermore, we show that the three atom finite Boolean Algebra has no triple of subalgebras whose weakly commuting property is destroyed when the exponential functor is applied.
dc.format.mimetypeapplication/pdf
dc.subjectthree-way commuting
dc.subjectsubalgebra triples
dc.subjectboolean subalgebras
dc.subjectcommuting property of boolean subalgebra triples
dc.subjectcommuting property of boolean algebras
dc.subjectcommuting boolean subalgebras
dc.subjectweakly commuting boolean subalgebra n-tuples
dc.subjectcommuting boolean subalgebra n-tuples
dc.subjectexponential functor
dc.subjectVietoris hyperspace
dc.subjectStone dual
dc.subjectStone Representation Theorem
dc.subjectFields
dc.subjectdestroying the commutativity property of finite boolean subalgebra triples
dc.subjectfour atom boolean algebra
dc.subjectthree atom boolean algebra
dc.subjectatomic boolean algebras
dc.subjectinheriting properties of boolean algebras
dc.subjectatom-wise inheritance of boolean algebra properties
dc.subjectinheriting the commuting property of boolean algebras
dc.subject.lcshAlgebra, Booleanen-US
dc.titleBreaking the Weak Commutative Property of Finite Boolean Subalgebra Triples
dc.typeThesis
dc.date.updated2017-04-28T14:46:26Z
dc.type.materialtext
thesis.degree.nameMaster of Science
thesis.degree.levelMasters
thesis.degree.disciplineMathematics
thesis.degree.grantorTexas A&M International University
thesis.degree.departmentMathematics & Physics
dc.creator.orcid0000-0002-6678-5678


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