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.
Publisher
Canadian Mathematical Society
Cited by
5 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献
1. The Nullstellensatz over p-adically closed fields;Journal of the Mathematical Society of Japan;1980-07-01
2. Riemann surfaces;Journal of Soviet Mathematics;1980-07
3. Global ideal theory of meromorphic function fields;Transactions of the American Mathematical Society;1979
4. Restricted ideals in rings of analytic functions;Bulletin of the American Mathematical Society;1974
5. Finitely generated ideals in rings of analytic functions;Mathematische Annalen;1971-10