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Rings of Meromorphic Functions on Non-Compact Riemann Surfaces

Published online by Cambridge University Press:  20 November 2018

James Kelleher
James Kelleher*
Affiliation:
Columbia University, New York, New York
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In this paper we shall be concerned with the algebraic structure of certain rings of functions meromorphic on a non-compact (connected) Riemann surface Ω. In this setting, A = A(Ω) and K= K(Ω) denote (respectively) the ring of all complex-valued functions analytic on Ω and its field of quotients, the field of functions meromorphic on Ω. The rings considered here are those subrings of K containing A,which we term A-rings of K. Most of the results given here were previously announced without proof (15) and are contained in the author's doctoral dissertation (16), completed at the University of Illinois under the direction of Professor M. Heins, whose encouragement and advice are gratefully acknowledged.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 21 , 1969 , pp. 284 - 300
Copyright
Copyright © Canadian Mathematical Society 1969

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