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 A_R(D) denote the set of functions belonging to the disc algebra having real Fourier coefficients. We show that A_R(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 A_R(D) to have Bass stable rank equal to 1.

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		CDAM Research Reports Series Centre for Discrete and Applicable Mathematics London School of Economics Houghton Street London WC2A 2AE, U.K.
		Phone: +44(0)-20-7955 7494. Fax: +44(0)-20-7955 6877. Email: info@maths.lse.ac.uk