Idempotente voortbringers van matriksalgebras
| dc.contributor.advisor | Van Wyk, L. | |
| dc.contributor.author | Marais, Magdaleen Suzanne | |
| dc.contributor.other | University of Stellenbosch. Faculty of Science. Dept. of Mathematical Sciences. | |
| dc.date.accessioned | 2008-04-09T06:15:11Z | en_ZA |
| dc.date.accessioned | 2010-06-01T08:41:27Z | |
| dc.date.available | 2008-04-09T06:15:11Z | en_ZA |
| dc.date.available | 2010-06-01T08:41:27Z | |
| dc.date.issued | 2007-12 | |
| dc.description | Thesis (MSc (Mathematics))--University of Stellenbosch, 2007. | |
| dc.description.abstract | 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]. | en |
| dc.format.extent | 504759 bytes | en_ZA |
| dc.format.mimetype | application/pdf | en_ZA |
| dc.identifier.uri | http://hdl.handle.net/10019.1/2146 | |
| dc.language.iso | af | |
| dc.publisher | Stellenbosch : University of Stellenbosch | |
| dc.rights.holder | University of Stellenbosch | |
| dc.subject | Dissertations -- Mathematics | en |
| dc.subject | Theses -- Mathematics | en |
| dc.subject | Idempotents | en |
| dc.subject | Matrices | en |
| dc.title | Idempotente voortbringers van matriksalgebras | af |
| dc.type | Thesis |