Henriksenʼs contributions to residue class rings of analytic and entire functions

The author surveys, summarizes and generalizes results of Golasiński and Henriksen, and of others, concerning certain residue class rings. ( R ) denote the ring of analytic functions over reals R and E ( K ) the ring of entire functions over R or complex numbers C . It is shown that if m is a maximal ideal of A ( R ) , then A ( R ) / m is isomorphic either to the reals or a real-closed field that is η 1 -set, while if m is a maximal ideal of E ( K ) , then E ( K ) / m is isomorphic to one of these latter two fields or to complex numbers.