\(h\)-divisible modules over integral domains
Let \(R\) be an integral domain which is not a field. In several previous papers, the author proved that there exist the following irreversible implications: \(\,h\)-divisible pure injective \(\Longrightarrow\) weak injective \(\Longrightarrow\) \(\,h\)-divisible. In Section 2 of the paper it is proved that it suffices to use these modules to determine the weak dimension of modules via Tor. In Section 3 various cotorsion modules which are \(\,h\)-divisible are considered, a series of irreversible implications between these modules are established, and characterizations of domains over which some particular implications are reversible. In Section 4 the author introduces copure-weak-injective modules as being those \(R\)-modules \(M\) for which Ext\(^1_R(D,M)=0\) for all weak-injective \(R\)-modules \(D\), and characterizes them over particular domains.
scientific article; zbMATH DE number 5931636
scientific article