Multiplication Rings Via Their Total Quotient Rings

Abstract

In the following paper ring will always mean commutative ring which may or may not have an identity. We use the letterNexclusively for nilpotents of the ringA.A ring such that, given any two idealsLandMwithL⊆Mthere exists an idealQsuch thatL=QMis called amultiplication ring. For references to early papers on multiplication rings by Krull and Mori the reader is referred to [2]. A ring in which every regular ideal is invertible is called aDedekind ring.