Multiplication rings as rings in which ideals with prime radical are primary

A commutative ring R is called an AM-ring (for allgemeine multiplikationsring) if whenever A and B are ideals of R with A properly contained in B, then there is an ideal C of R such that A = BC.An AM-ring R in which RA = A for each ideal A of R is called a multiplication ring.Krull introduced the notion of a multiplication ring in [11], [13].Akizuki is responsible for the more general concept of an AM-ring in [l], but Mori has developed most of the structure theory for such rings in [14], [15], [16], [17], and [18].An important property of an AM-ring R is that R satisfies what Gilmer called condition ( *) in [ 7 ] and [ 8 ] : A n ideal of R with prime radical is primary.In §1, new results concerning rings in which (*) holds are given.These are applied to obtain structure theorems for AM-rings in §2.