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The categorical and algebraic aspects of near-modules and near-vector spaces
Thesis (MSc)--Stellenbosch University, 2023.
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| Other Authors: | |
| Format: | Thesis |
| Language: | en_ZA |
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Stellenbosch : Stellenbosch University
2023
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| _version_ | 1867613966877851648 |
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| access_status_str | Open Access |
| author | Moore, Daniella |
| author2 | Janelidze, Zurab |
| author_browse | Janelidze, Zurab Moore, Daniella |
| author_facet | Janelidze, Zurab Moore, Daniella |
| author_sort | Moore, Daniella |
| collection | Thesis |
| dc_rights_str_mv | Stellenbosch University |
| description | Thesis (MSc)--Stellenbosch University, 2023. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/127400 |
| institution | Stellenbosch University (South Africa) |
| language | en_ZA |
| last_indexed | 2026-06-10T12:44:33.029Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2023 |
| publishDateRange | 2023 |
| publishDateSort | 2023 |
| publisher | Stellenbosch : Stellenbosch University |
| publisherStr | Stellenbosch : Stellenbosch University |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/127400 The categorical and algebraic aspects of near-modules and near-vector spaces Moore, Daniella Janelidze, Zurab Marques, Sophie Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. near-vector spaces Vector spaces Finite fields (Algebra) Modules (Algebra) UCTD Thesis (MSc)--Stellenbosch University, 2023. ENGLISH 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. AFRIKAANSE 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. Masters 2023-03-07T18:39:41Z 2023-05-18T07:20:15Z 2023-03-07T18:39:41Z 2023-05-18T07:20:15Z 2023-03 Thesis http://hdl.handle.net/10019.1/127400 en_ZA Stellenbosch University v, 67 pages application/pdf Stellenbosch : Stellenbosch University |
| spellingShingle | near-vector spaces Vector spaces Finite fields (Algebra) Modules (Algebra) UCTD Moore, Daniella The categorical and algebraic aspects of near-modules and near-vector spaces |
| title | The categorical and algebraic aspects of near-modules and near-vector spaces |
| title_full | The categorical and algebraic aspects of near-modules and near-vector spaces |
| title_fullStr | The categorical and algebraic aspects of near-modules and near-vector spaces |
| title_full_unstemmed | The categorical and algebraic aspects of near-modules and near-vector spaces |
| title_short | The categorical and algebraic aspects of near-modules and near-vector spaces |
| title_sort | categorical and algebraic aspects of near modules and near vector spaces |
| topic | near-vector spaces Vector spaces Finite fields (Algebra) Modules (Algebra) UCTD |
| url | http://hdl.handle.net/10019.1/127400 |
| work_keys_str_mv | AT mooredaniella thecategoricalandalgebraicaspectsofnearmodulesandnearvectorspaces AT mooredaniella categoricalandalgebraicaspectsofnearmodulesandnearvectorspaces |