ON THE UNIT-1-STABLE RANK OF RINGS OF ANALYTIC FUNCTIONS

In this paper we prove a general result for the ring H(U) of the analytic functions on an open set U in the complex plane which implies that H(U) has not unit-1-stable rank and that has some other interesting consequences. We prove also that in H(U) there is no totally reducible elements different f...

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Bibliographic Details
Published in:Publicacions matemàtiques 1992-01, Vol.36 (2A), p.439-447
Main Authors: Carmona, Joan Josep, Cufí, Julià, Menal, Pere
Format: Article
Language:English
Subjects:
Algebra
Analytic functions
Mathematical functions
Mathematical rings
Mathematical theorems
Multiplicity of function roots
Polynomials
Von Neumann algebra
Zero
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Summary:In this paper we prove a general result for the ring H(U) of the analytic functions on an open set U in the complex plane which implies that H(U) has not unit-1-stable rank and that has some other interesting consequences. We prove also that in H(U) there is no totally reducible elements different from the zero function.
ISSN:0214-1493
2014-4350
DOI:10.5565/PUBLMAT_362A92_08