Prime ideals surviving in complete integral closures (Q1383599)

A domain \(R\) is called Archimedean if for every non-unit \(x\in R\), \(\bigcap Rx^n=0\). This paper studies when every prime ideal of a given domain \(R\) survives (that is, remains proper) when one goes up to its complete integral closure. The author proves amongst other things that if \(R\) is an Archimedean domain such that every finitely generated proper ideal is contained in the radical of a proper principal ideal, then the above property is indeed true.