On Rings over Which All Modules Are Direct Sums of Distributive Modules

A module is said to be $\mathsf{\text{distributive}}$ if the lattice of its submodules is distributive. A direct sum of distributive modules is called a $\mathsf{\text{semidistributive}}$ module. In this paper we consider rings $A$ such that all right $A$-modules are semidistributive.