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The cone and cylinder algebras. (English) Zbl 1344.46037

Summary: In this exposition-type note we present detailed proofs of certain assertions concerning several algebraic properties of the cone and cylinder algebras. These include a determination of the maximal ideals, the solution of the Bézout equation, and a computation of the stable ranks by elementary methods.

MSC:

46J10 Banach algebras of continuous functions, function algebras
46J15 Banach algebras of differentiable or analytic functions, \(H^p\)-spaces
46J20 Ideals, maximal ideals, boundaries
30H50 Algebras of analytic functions of one complex variable
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