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We determine, via classroom proofs, the maximal ideal space, the Bass stable rank as well as the topological and dense stable rank of the uniform closure of all complex-valued functions continuously differentiable on neighborhoods of a compact planar set K and holomorphic in the interior K∘ of K. In this spirit, we also give elementary approaches to the calculation of these stable ranks for some classical function algebras on K.

A Note on Some Uniform Algebra Generated by Smooth Functions in the Plane