  R is called a right WV -ring if each simple right R-module is injective
relative to proper cyclics. If R is a right WV -ring, then R is right uniform
or a right V -ring. It is shown that for a right WV-ring R, R is right
noetherian if and only if each right cyclic module is a direct sum of a
projective module and a CS or noetherian module. For a finitely generated
module M with projective socle over a V -ring R such that every subfactor of M
is a direct sum of a projective module and a CS or noetherian module, we show M
= X \oplus T, where X is semisimple and T is noetherian with zero socle. In the
case that M = R, we get R = S \oplus T, where S is a semisimple artinian ring,
and T is a direct sum of right noetherian simple rings with zero socle. In
addition, if R is a von Neumann regular ring, then it is semisimple artinian.
