Centre for Discrete and Applicable Mathematics 

CDAM Research Report, LSECDAM200516December 2005 
On the coherence of some irrational transfer function classes
Amol Sasane
Abstract
Let D, T denote the unit disc and unit circle with center 0, respectively, in the complex plane C. If S is a subset of T, then let A_S denote the set of complexvalued functions defined on D U S, that are analytic in D, and continuous and bounded on D U 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.
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