International Journal of Mathematics and Mathematical Sciences 
Volume 12 (1989), Issue 1, Pages 65-68
doi:10.1155/S0161171289000086

A characterization of the algebra of holomorphic functions on a simply connected domain

Derming Wang and Saleem Watson

 Department of Mathematics and Computer Science, California State University, Long Beach 90840, California, USA
Received 3 August 1987

Abstract

Let A be a singly-generated ℱ-algebra. It is shown that A isomorphic to H(Ω) where Ω is a simply connected domain in ℂ if and only if A has no topological divisors of zero. It follows from this that there are exactly three ℱ-algebras (up to isomorphism) which are singly generated and have no topological divisors of zero.