  Let $A$ be a ring with minimum condition on principal right ideals. It is
proved that $\aleph_0$-distributive right (left) $A$-modules coincide with
Artinian (Noetherian) right (left) $A$-modules. Rings, over which all right
modules are direct sums of $\aleph_0$-distributive coincide with rings of of
finite representation type. Rings, whose right modules are semidistributive,
coincide with Kawada rings, over basis rings of which all right modules are
completely cyclic. The studies of Tuganbaev are supported by Russian Scientific
Foundation, project 22-11-00052.
