Maximally Prüfer Rings

Abstract

In this paper we consider six Prüfer-like conditions on a commutative ring R, and introduce seventh condition by defining the ring R to be maximally Prüfer if R M is Prüfer for every maximal ideal M of R, and we show that the class of such rings lie properly between Prüfer rings and locally Prüfer rings. We give a characterization of such rings in terms of the total quotient ring and the core of the regular maximal ideals. We also find a relationship of such rings with strong Prüfer rings.