Pseudo-valuation rings (Q2785914)

The aim of this paper is to generalize the theory of pseudo-valuation domains (PVD) to commutative rings with identity. The authors define a pseudo-valuation ring (PVR) as a ring where each prime ideal \(P\) is strongly prime, i.e. a prime ideal such that whenever \(a,b \in R\) then \(aP\) and \(bP\) are comparable. They extend known results on PVD, study the stability of the class of PVRs under passage to overrings and decide when the integral closure of a PVR \((R,M)\) equals \((M:M)\).NEWLINENEWLINEFor the entire collection see [Zbl 0855.00015].