# Idempotente voortbringers van matriksalgebras

Thesis (MSc (Mathematics))--University of Stellenbosch, 2007.

Thesis

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].