a1 University of Iowa and University of Nebraska
In a recent paper  one of the authors has introduced the concept of module type of a ring, for rings with unit. The object of this paper is to generalize this concept to arbitrary rings, without assuming the existence of a unit. This is easily accomplished for rings with one-sided unit, and we shall define the type of such a ring. Theorem 2.5 gives a relation between this type and the module type of , and permits the immediate extension of all results in  to rings with one-sided unit.
(Received September 23 1964)