In this paper, we study approximately Cohen-Macaulay rings, give a series of equivalent conditions for a Noetherian ring to be a approximately Cohen-Macaulay ring and estimate its Samuel functions with respect to some definition ideal.

• Approximately Cohen－Macaulay Rings and Samuel FunctionsWangFuzheng（王福正）（DepartmentofMathematics，PeikingUniversityBeijing，1008...