Contributions to the theory of near-vector spaces

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dc.contributor.advisorHowell, Karin-Thereseen_ZA
dc.contributor.authorSanon, Sogo Pierreen_ZA
dc.contributor.otherStellenbosch University. Faculty of Science. Dept. of Mathematical Sciences.en_ZA
dc.date.accessioned2017-11-27T08:34:20Z
dc.date.accessioned2017-12-11T11:06:20Z
dc.date.available2017-11-27T08:34:20Z
dc.date.available2017-12-11T11:06:20Z
dc.date.issued2017-12
dc.descriptionThesis (MSc)--Stellenbosch University, 2017en_ZA
dc.description.abstractENGLISH ABSTRACT : The purpose of this thesis is to give an exposition and expand the theory of near-vector spaces. Near-vector space theory is a new and rich field of mathematics and has been used in several applications, including in secret sharing schemes in cryptography and to construct interesting new examples of planar near-rings. There are two type of near-vector spaces, we focus on the near-vector space defined by André in [2]. After giving several elementary definitions and properties in Chapter 2, we present the theory of nearvector spaces in Chapter 3. In [13] van der Walt showed how to construct an arbitrary finite-dimensional near-vector space, using a finite number of near-fields, all having isomorphic multiplicative semigroups. The majority of the results did not contain complete proofs and explanation. Chapter 4 is dedicated to the proofs and explanations of these results. In Chapter 5 we investigate the linear mappings of near-vector spaces. New results are presented in this section which have been accepted for publication.en_ZA
dc.description.abstractAFRIKAANSE OPSOMMING : Die doel van hierdie tesis is om ’n uiteensetting en uitbreiding van die teorie van byna-vektorruimtes te gee. Die teorie van byna-vektorruimtes is ’n nuwe en ryk veld van wiskunde wat al in verskeie toepassings gebruik is, insluitend geheimdelingskemas in kriptografie en om nuwe interessante voorbeelde van planêre bynaringe te konstruktueer. Daar is twee tipes byna-vektorruimtes, ons fokus op die een gedefinieer deur André in [2]. Na ons in Hoofstuk 2 verskeie elementêre definisies en eienskappe gegee het, bied ons die teorie van byna-vektorruimtes in Hoofstuk 3 aan. In [13] het van der Walt gewys hoe om ’n arbitrêre eindig-dimensionele byna-vektorruimte te konstrueer deur gebruik te maak van ’n eindige aantal byna-liggame, met isomorfe vermenigvuldings semi-groepe. Die meerderheid van die resultate het nie volledige bewyse en verduidelikings bevat nie. Hoofstuk 4 is toegewy aan die bewyse en verduidelikings van hierdie resultate. In Hoofstuk 5 ondersoek ons die lineêre afbeeldings van byna-vektorruimtes. Nuwe resultate wat reeds vir publikasie goedgekeur is, word in hierdie afdeling aangebied.af_ZA
dc.format.extentix, 78 pagesen_ZA
dc.identifier.urihttp://hdl.handle.net/10019.1/102872
dc.language.isoen_ZAen_ZA
dc.publisherStellenbosch : Stellenbosch Universityen_ZA
dc.rights.holderStellenbosch Universityen_ZA
dc.subjectAlgebras, Linearen_ZA
dc.subjectUCTDen_ZA
dc.subjectCryptographyen_ZA
dc.subjectNear-vector spacesen_ZA
dc.subjectVector spacesen_ZA
dc.titleContributions to the theory of near-vector spacesen_ZA
dc.typeThesisen_ZA
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