The categorical and algebraic aspects of near-modules and near-vector spaces

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dc.contributor.advisorJanelidze, Zuraben_ZA
dc.contributor.advisorMarques, Sophieen_ZA
dc.contributor.authorMoore, Daniellaen_ZA
dc.contributor.otherStellenbosch University. Faculty of Science. Dept. of Mathematical Sciences.en_ZA
dc.date.accessioned2023-03-07T18:39:41Z
dc.date.accessioned2023-05-18T07:20:15Z
dc.date.available2023-03-07T18:39:41Z
dc.date.available2023-05-18T07:20:15Z
dc.date.issued2023-03
dc.descriptionThesis (MSc)--Stellenbosch University, 2023.en_ZA
dc.description.abstractENGLISH SUMMARY: In this thesis we generalize some results from vector spaces to near-vector spaces in the sense of J. André. In particular, we establish the First Isomorphism Theorem, which leads us to proving that the category of near-vector spaces is an abelian category. We also include an algebraic proof of the non-trivial fact that a subspace of a near-vector space is itself a near-vector space. Other algebraic and categorical properties of near-vector spaces are also obtained.en_ZA
dc.description.abstractAFRIKAANSE OPSOMMING: In hierdie tesis veralgemeen ons sommige resultate van vektorruimtes na byna-vektorruimtes in die sin van J. André. Ons maak spesifiek die Eerste Isomorfisme Stelling, wat ons daartoe lei om te bewys dat die kategorie van byna-vektorruimtes ’n Abelse kategorie is. Ons sluit ook algebraiese bewys in van die nie-triviale feit dat ’n subruimte van ’n bynavektorruimte op sigself ’n byna-vektorruimte is. Ander algebraiese en kategorie eienskappe van byna-vektorruimtes word ook verkry.af_ZA
dc.description.versionMasters
dc.format.extentv, 67 pages
dc.identifier.urihttp://hdl.handle.net/10019.1/127400
dc.language.isoen_ZAen_ZA
dc.publisherStellenbosch : Stellenbosch University
dc.rights.holderStellenbosch University
dc.subjectnear-vector spacesen_ZA
dc.subject.lcshVector spacesen_ZA
dc.subject.lcshFinite fields (Algebra)en_ZA
dc.subject.lcshModules (Algebra)en-ZA
dc.subject.nameUCTD
dc.titleThe categorical and algebraic aspects of near-modules and near-vector spacesen_ZA
dc.typeThesisen_ZA
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