A class of Prüfer domains that are similar to the ring of entire functions (Q1288325)

Let \(R\) denote the ring of entire functions For any complex number \(\alpha\), let \(M_\alpha\) denote the ideal of \(R\) generated by the polynomial \(z-\alpha\). In this paper, the author defines a class of domains called \(E\)-domains which are obtained by intersecting Noetherian valuation domains in such a way that the centres of the defining valuation domains behave like the ideals \(M_\alpha\) of \(R\). It is shown that an \(E\)-domain has many properties in common with \(R\). Comparison with the prime ideals as well as divisorial ideals of an \(E\)-domain and of \(R\) is drawn. The paper also contains a number of interesting open problems regarding \(E\)-domains.