On the stable rank and reducibility in algebras of real symmetric functions
R Rupp, A Sasane - Mathematische Nachrichten, 2010 - Wiley Online Library
Abstract Let Aℝ (𝔻) denote the set of functions belonging to the disc algebra having real
Fourier coefficients. We show that Aℝ (𝔻) has Bass and topological stable ranks equal to 2,
which settles the conjecture made by Brett Wick in [18]. We also give a necessary and
sufficient condition for reducibility in some real algebras of functions on symmetric domains
with holes, which is a generalization of the main theorem in [18]. A sufficient topological
condition on the symmetric open set 𝔻 is given for the corresponding real algebra Aℝ (𝔻) to …
Fourier coefficients. We show that Aℝ (𝔻) has Bass and topological stable ranks equal to 2,
which settles the conjecture made by Brett Wick in [18]. We also give a necessary and
sufficient condition for reducibility in some real algebras of functions on symmetric domains
with holes, which is a generalization of the main theorem in [18]. A sufficient topological
condition on the symmetric open set 𝔻 is given for the corresponding real algebra Aℝ (𝔻) to …
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