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Bulletin of the London Mathematical Society Advance Access originally published online on July 10, 2009
Bulletin of the London Mathematical Society 2009 41(4):669-675; doi:10.1112/blms/bdp057
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© 2009 London Mathematical Society

Ideals of denominators in the disk-algebra

Raymond Mortini

Département de Mathématiques et LMAM
Université Paul Verlaine
Ile du Saulcy, F-57045 Metz
France
mortini@math.univ-metz.fr

Amol Sasane

Department of Mathematics
London School of Economics
Houghton Street
London
WC2A 2AE
United Kingdom

Received 30 June 2008. Revision received 24 March 2009.

We show that there do not exist finitely generated, non-principal ideals of denominators in the disk-algebra A(D). Our proof involves a new factorization theorem for A(D) that is based on Treil's determination of the Bass stable rank for H{infty}.

2000 Mathematics Subject Classification 46J15 (primary), 30D50 (secondary).


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