Some results about proper overrings of pseudo-valuation domains

Abstract

Let [Formula: see text] be a (unital) extension of (commutative) rings. We say that [Formula: see text] is a maximal non-quasi-local (respectively, non-PVD) subring of [Formula: see text] if [Formula: see text] is not quasi-local (respectively, PVD) and each subring of [Formula: see text] properly containing [Formula: see text] is quasi-local (respectively, PVD). The aim of this paper is to study this kind of ring extensions and to investigate the structure of the intermediate rings between [Formula: see text] and [Formula: see text].