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

Rupp, R. and Sasane, Amol (2010) On the stable rank and reducibility in algebras of real symmetric functions. Mathematische Nachrichten, 283 (8). pp. 1194-1206. ISSN 0025-584X

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Identification Number: 10.1002/mana.200710080


Let Aℝ([MATHEMATICAL DOUBLE-STRUCK CAPITAL D]) denote the set of functions belonging to the disc algebra having real Fourier coefficients. We show that Aℝ([MATHEMATICAL DOUBLE-STRUCK CAPITAL 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 [MATHEMATICAL DOUBLE-STRUCK CAPITAL D] is given for the corresponding real algebra Aℝ([MATHEMATICAL DOUBLE-STRUCK CAPITAL D]) to have Bass stable rank equal to 1.

Item Type: Article
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Additional Information: © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Date Deposited: 28 Jul 2011 09:17
Last Modified: 16 May 2024 01:08

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