Derming Wang, Saleem Watson, "A characterization of the algebra of holomorphic functions on a simply connected domain", International Journal of Mathematics and Mathematical Sciences, vol. 12, Article ID 463292, 4 pages, 1989. https://doi.org/10.1155/S0161171289000086
A characterization of the algebra of holomorphic functions on a simply connected domain
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.
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