h-Divisible modules over integral domains

Over integral domains, we characterize modules of finite weak dimension ⩽n in terms of h-divisible pure-injective modules (Theorems 2.1 and 2.2). We compare various classes of h-divisible modules in terms of cotorsion modules (Theorems 3.1 through 3.11). We also introduce copure-weak-injective modules and characterize them over certain domains (Theorems 4.3 and 4.6). We characterize the modules that are pure in their weak-injective envelopes in Proposition 4.12.