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Idempotente voortbringers van matriksalgebras
Thesis (MSc (Mathematics))--University of Stellenbosch, 2007.
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| Format: | Thesis |
| Language: | Afrikaans |
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Stellenbosch : University of Stellenbosch
2008
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| _version_ | 1867613884046639104 |
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| access_status_str | Open Access |
| author | Marais, Magdaleen Suzanne |
| author2 | Van Wyk, L. |
| author_browse | Marais, Magdaleen Suzanne Van Wyk, L. |
| author_facet | Van Wyk, L. Marais, Magdaleen Suzanne |
| author_sort | Marais, Magdaleen Suzanne |
| collection | Thesis |
| dc_rights_str_mv | University of Stellenbosch |
| description | Thesis (MSc (Mathematics))--University of Stellenbosch, 2007. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/2146 |
| institution | Stellenbosch University (South Africa) |
| language | Afrikaans |
| last_indexed | 2026-06-10T12:43:13.574Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2008 |
| publishDateRange | 2008 |
| publishDateSort | 2008 |
| publisher | Stellenbosch : University of Stellenbosch |
| publisherStr | Stellenbosch : University of Stellenbosch |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/2146 Idempotente voortbringers van matriksalgebras Marais, Magdaleen Suzanne Van Wyk, L. University of Stellenbosch. Faculty of Science. Dept. of Mathematical Sciences. Dissertations -- Mathematics Theses -- Mathematics Idempotents Matrices Thesis (MSc (Mathematics))--University of Stellenbosch, 2007. An exposition is given of [12], a paper by N. Krupnik, which is a discussion of the minimum number of idempotent generators of a complete matrix algebra Mn(F) over a field F, as well as direct sums of complete matrix algebras over F. It will, for example, be proved that, if n ≥ 2, then the minimum number of idempotent generators of a n × n matrix algebra is equal to 2 or 3. Krupnik made an incorrect statement in ([12], Theorem 5), namely that the minimum number of idempotent generators of m copies of an infinite field F, as an algebra over F, is m−1. This error was identified and corrected by A.V. Kelarev, A.B. van der Merwe and L. van Wyk in [11]. The thesis also includes an exposition of this correction. Furthermore an exposition will be given of the main result of [5], where E. Formanek showed that, if n ≥ 2, then there is a non-vanishing central polynomial for Mn(F), with F any field. The last mentioned result will be used in the exposition of [12]. 2008-04-09T06:15:11Z 2010-06-01T08:41:27Z 2008-04-09T06:15:11Z 2010-06-01T08:41:27Z 2007-12 Thesis http://hdl.handle.net/10019.1/2146 af University of Stellenbosch 504759 bytes application/pdf application/pdf Stellenbosch : University of Stellenbosch |
| spellingShingle | Dissertations -- Mathematics Theses -- Mathematics Idempotents Matrices Marais, Magdaleen Suzanne Idempotente voortbringers van matriksalgebras |
| title | Idempotente voortbringers van matriksalgebras |
| title_full | Idempotente voortbringers van matriksalgebras |
| title_fullStr | Idempotente voortbringers van matriksalgebras |
| title_full_unstemmed | Idempotente voortbringers van matriksalgebras |
| title_short | Idempotente voortbringers van matriksalgebras |
| title_sort | idempotente voortbringers van matriksalgebras |
| topic | Dissertations -- Mathematics Theses -- Mathematics Idempotents Matrices |
| url | http://hdl.handle.net/10019.1/2146 |
| work_keys_str_mv | AT maraismagdaleensuzanne idempotentevoortbringersvanmatriksalgebras |