Noncoherence of some rings of functions
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Abstract:
Let $\mathbb D$, $\mathbb T$ denote the unit disc and unit circle, respectively, in $\mathbb C$, with center $0$. If $S\subset \mathbb T$, then let $A_{S}$ denote the set of complex-valued functions defined on $\mathbb D\cup S$ that are analytic in $\mathbb D$, and continuous and bounded on $\mathbb D\cup S$. Then $A_{S}$ is a ring with pointwise addition and multiplication. We prove that if the intersection of $S$ with the set of limit points of $S$ is not empty, then the ring $A_{S}$ is not coherent.References
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Additional Information
- Amol Sasane
- Affiliation: Department of Mathematics, London School of Economics, Houghton Street, London WC2A 2AE, United Kingdom
- Email: A.J.Sasane@lse.ac.uk
- Received by editor(s): September 20, 2005
- Received by editor(s) in revised form: March 10, 2006
- Published electronically: February 6, 2007
- Communicated by: Joseph A. Ball
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 2107-2111
- MSC (2000): Primary 46J15, 30A98; Secondary 93C05, 13E15
- DOI: https://doi.org/10.1090/S0002-9939-07-08704-7
- MathSciNet review: 2299487