On the stable rank and reducibility in algebras of real symmetric functions

✍ Scribed by R. Rupp; A. Sasane

• Publisher: John Wiley and Sons
• Year: 2010
• Tongue: English
• Weight: 172 KB
• Volume: 283
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.200710080

✦ Synopsis

Abstract

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 (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)