On the Krull intersection theorem in function algebras

Abstract

A version of the Krull intersection theorem states that for Noetherian integral domains the Krull intersection ki(I) of every proper ideal I is trivial; that is

            ∞

ki(I) := ∩ Iⁿ = {0}

           n=1

We investigate the validity of this result for various function algebras R, present ideals I of R for which ki(I) ≠ {0}, and give conditions on I so that ki(I) = {0}.

Keywords: Function algebras, Krull intersection theorem, bounded analytic functions