Primary ideals in rings of analytic functions

Williams, R. Douglas

doi:10.1090/S0002-9947-1973-0320760-6

Primary ideals in rings of analytic functions
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by R. Douglas Williams

Trans. Amer. Math. Soc. 177 (1973), 37-49

DOI: https://doi.org/10.1090/S0002-9947-1973-0320760-6

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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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