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].
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:sun/oai:scholar.sun.ac.za:10019.1/2146 |
| Date | 12 1900 |
| Creators | Marais, Magdaleen Suzanne |
| Contributors | Van Wyk, L., University of Stellenbosch. Faculty of Science. Dept. of Mathematical Sciences. |
| Publisher | Stellenbosch : University of Stellenbosch |
| Source Sets | South African National ETD Portal |
| Language | Afrikaans |
| Detected Language | English |
| Type | Thesis |
| Format | 504759 bytes, application/pdf |
| Rights | University of Stellenbosch |
Page generated in 0.0021 seconds