Rings of Meromorphic Functions on Non-Compact Riemann Surfaces
Author:
- James KelleherJKJames Kelleher
- 1 January 1969
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 21, 284-300
Abstract
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.Keywords
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