Denumerable distributivity, linear compactness and condition \(AB5^*\) in modules (Q1375001)

The problem of the characterization of rings over which all right modules are direct sums of distributive modules was solved by Fuller and Tuganbaev. The basic result of this paper (Theorem 2) provides a solution to the similar problem where distributive modules are replaced by \(AB5^*\)-modules. As a corollary, the author obtains the negative answer to the question whether it is possible to define a linearly compact module in terms of the lattice of its submodules (Corollary 3).