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

## Abstract

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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Official URL: | http://www.wiley-vch.de/publish/en/journals/alphab... |

Additional Information: | © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim |

Library of Congress subject classification: | Q Science > QA Mathematics |

Sets: | Departments > Mathematics |

Rights: | http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx |

Date Deposited: | 28 Jul 2011 09:17 |

URL: | http://eprints.lse.ac.uk/37643/ |

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