Closed ideals in a new class of algebras of holomorphic functions on the disc

We define a new class of Banach algebras of holomorphic functions on the unit disc $\mathbb{D}$ which contains the algebras studied in [GMR2] and [GW]. To a function G of the class ${\mathcal{A}}^1(\mathbb{D})$ nowhere vanishing in $\mathbb{D}$ we associate a Banach algebra ${\mathcal{A}}_G^n(\mathbb{D})$ contained in the disc algebra $\mathcal{A}(\mathbb{D})$. We prove that all closed ideals of ${\mathcal{A}}_G^n(\mathbb{D})$ of at most countable hull are of the standard form.