摘要： A Class M of rings is said to be weakly hereditary if 0÷I<R∈M implies 0≠I"∈M for some positive integer n,which generalizes the concept of heredity but other than that of regularity.In §2 the properties of such class and its essential cover are studied.In §3 the upper radicals determined by them are investigated,At the same time the “Problem 42, 44 and 55” of Szasz [7] are discussed.In §4 two examples are given, which show that the concept of weak heredity is independent of that of regularity.
