Idempotente voortbringers van matriksalgebras

[摘要] An exposition is given of [12], a paper by N. Krupnik, which is a discussion of the minimumnumber of idempotent generators of a complete matrix algebra Mn(F) over a field F, aswell as direct sums of complete matrix algebras over F. It will, for example, be provedthat, if n ≥ 2, then the minimum number of idempotent generators of a n × n matrixalgebra 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 fieldF, 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 ofthis correction. Furthermore an exposition will be given of the main result of [5], whereE. Formanek showed that, if n ≥ 2, then there is a non-vanishing central polynomial forMn(F), with F any field. The last mentioned result will be used in the exposition of [12].

[发布机构] Stellenbosch University