Noncoherence of some rings of functions |
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| Authors: | Amol Sasane |
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| Affiliation: | Department of Mathematics, London School of Economics, Houghton Street, London WC2A 2AE, United Kingdom |
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| Abstract: | Let  ,  denote the unit disc and unit circle, respectively, in  , with center 0. If  , then let  denote the set of complex-valued functions defined on  that are analytic in  , and continuous and bounded on  . Then  is a ring with pointwise addition and multiplication. We prove that if the intersection of  with the set of limit points of  is not empty, then the ring  is not coherent. |
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| Keywords: | Banach algebras of analytic functions coherent rings |
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