In [1, Theorem 2.3], it is proved that if R is an integral domain and M is a faithful multiplication
R-module, then M is a Prüfer module if and only if every finitely generated submodule
of M is principal. In this paper we prove that if M is a non zero faithful multiplication Rmodule,
then R is a Prüfer module if and only if R is an integral domain and every finitely
generated submodule of M is join-quasi-cyclic (i.e., join principal). Next we show that if M is
a non zero faithful multiplication R-module, then R is a Dedekind module if and only if R is an
integral domain and every submodule of M is a finitely generated join-quasi-cyclic submodule
of M.