Vol. 33, No. 1, 1970

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Rings of analytic functions

Julianne Souchek

Vol. 33 (1970), No. 1, 233–240

If F is an open Riemann surface and A(F) is the set of all analytic functions on F, then A(F) is a ring under pointwise addition and multiplication. This paper is concerned with proper subrings R of A(F) which are isomorphic images of A(G), the ring of all analytic functions on an open Riemann surface G, under a homomorphism Φ which maps constant functions onto themselves. The ring R has the form {g ∘ϕ: g A(G), ϕ an analytic map from F into G}, and will be denoted Rϕ. Relations between ϕ, Rϕ and the spectrum of R are given as necessary and sufficient conditions for the existence of a Riemann surface G such that R is isomorphic to A(G).

Mathematical Subject Classification
Primary: 30.87
Received: 24 July 1968
Revised: 14 October 1969
Published: 1 April 1970
Julianne Souchek