CDAM: Computational, Discrete and Applicable Mathematics@LSE

 CDAM Research Report, LSE-CDAM-2007-20

August 2007

On the Stable Rank and Reducibility in Algebras of Real Symmetric Functions

R. Rupp and A. Sasane

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 have Bass stable rank equal to 1.

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