International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 2, Pages 401-402

A generalization of Gelfand-Mazur theorem

Sung Guen Kim

Department of Mathematics, Pohang Institute of Science and Technology, P.O. Box 215, Pohang 790-600, Korea

Received 12 August 1991; Revised 19 November 1991

Copyright © 1993 Sung Guen Kim. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this paper, we show that if A is a unital semisimple complex Banach algebra with only the trivial idempotents and if σA(x) is countable for each xFr(G(A)), then AC, this generalizes the Gelfand-Mazur theorem.