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Contributions to the theory of near-vector spaces
Thesis (MSc)--Stellenbosch University, 2017
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| Format: | Thesis |
| Language: | en_ZA |
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Stellenbosch : Stellenbosch University
2017
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| _version_ | 1867613903234531328 |
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| access_status_str | Open Access |
| author | Sanon, Sogo Pierre |
| author2 | Howell, Karin-Therese |
| author_browse | Howell, Karin-Therese Sanon, Sogo Pierre |
| author_facet | Howell, Karin-Therese Sanon, Sogo Pierre |
| author_sort | Sanon, Sogo Pierre |
| collection | Thesis |
| dc_rights_str_mv | Stellenbosch University |
| description | Thesis (MSc)--Stellenbosch University, 2017 |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/102872 |
| institution | Stellenbosch University (South Africa) |
| language | en_ZA |
| last_indexed | 2026-06-10T12:43:32.400Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2017 |
| publishDateRange | 2017 |
| publishDateSort | 2017 |
| publisher | Stellenbosch : Stellenbosch University |
| publisherStr | Stellenbosch : Stellenbosch University |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/102872 Contributions to the theory of near-vector spaces Sanon, Sogo Pierre Howell, Karin-Therese Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. Algebras, Linear UCTD Cryptography Near-vector spaces Vector spaces Thesis (MSc)--Stellenbosch University, 2017 ENGLISH 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. AFRIKAANSE 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. 2017-11-27T08:34:20Z 2017-12-11T11:06:20Z 2017-11-27T08:34:20Z 2017-12-11T11:06:20Z 2017-12 Thesis http://hdl.handle.net/10019.1/102872 en_ZA Stellenbosch University ix, 78 pages application/pdf Stellenbosch : Stellenbosch University |
| spellingShingle | Algebras, Linear UCTD Cryptography Near-vector spaces Vector spaces Sanon, Sogo Pierre Contributions to the theory of near-vector spaces |
| title | Contributions to the theory of near-vector spaces |
| title_full | Contributions to the theory of near-vector spaces |
| title_fullStr | Contributions to the theory of near-vector spaces |
| title_full_unstemmed | Contributions to the theory of near-vector spaces |
| title_short | Contributions to the theory of near-vector spaces |
| title_sort | contributions to the theory of near vector spaces |
| topic | Algebras, Linear UCTD Cryptography Near-vector spaces Vector spaces |
| url | http://hdl.handle.net/10019.1/102872 |
| work_keys_str_mv | AT sanonsogopierre contributionstothetheoryofnearvectorspaces |