Idempotente voortbringers van matriksalgebras
Date
2007-12
Authors
Marais, Magdaleen Suzanne
Journal Title
Journal ISSN
Volume Title
Publisher
Stellenbosch : University of Stellenbosch
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].
Description
Thesis (MSc (Mathematics))--University of Stellenbosch, 2007.
Keywords
Dissertations -- Mathematics, Theses -- Mathematics, Idempotents, Matrices