Some results about proper overrings of pseudo-valuation domains

摘要

Let R subset of S be a (unital) extension of (commutative) rings. We say that R is a maximal non-quasi-local (respectively, non-PVD) subring of S if R is not quasi-local (respectively, PVD) and each subring of S properly containing R 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 R and S.