Multiplication Rings as Rings in Which Ideals with Prime Radical are Primary

Robert W. Gilmer, Joe Leonard Mott
1965 Transactions of the American Mathematical Society  
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 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
more » ... [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.
doi:10.2307/1993985 fatcat:eudliutf5neg3plyxkd3jzn77i