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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Primary ideals in rings of analytic functions


Author: R. Douglas Williams
Journal: Trans. Amer. Math. Soc. 177 (1973), 37-49
MSC: Primary 46J20; Secondary 13C05, 30A98
DOI: https://doi.org/10.1090/S0002-9947-1973-0320760-6
MathSciNet review: 0320760
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Abstract: Let A be the ring of all analytic functions on a connected, noncompact Riemann surface. We use the valuation theory of the ring A as developed by N. L. Alling to analyze the structure of the primary ideals of A. We characterize the upper and lower primary ideals of A and prove that every nonprime primary ideal of A is either an upper or a lower primary ideal. In addition we give some necessary and sufficient conditions for certain ideals of A to be intersections of primary ideals.


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DOI: https://doi.org/10.1090/S0002-9947-1973-0320760-6
Keywords: Rings of analytic functions, primary ideals, intersections of prime ideals, intersections of primary ideals, rings of continuous functions
Article copyright: © Copyright 1973 American Mathematical Society

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