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 simply connected domain

Abstract

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