In this paper a ring will always mean a commutative ring with identity element. Furthermore, a ring R is called a multiplication ring if, whenever A and B are ideals of R and A is contained in B, there is an ideal C such that A = BC. Noetherian multiplication rings have been studied by Asano (1), Krull (4, 5), and Mori (6, 7). Krull also studied non-Noetherian multiplication rings (3). In (8, 9), Mori studied non-Noetherian multiplication rings which did not necessarily contain an identity element.