  We show that the quasiequational theory of a relatively congruence modular
quasivariety of left $R$-modules is determined by a two-sided ideal in $R$
together with a filter of left ideals. The two-sided ideal encodes the
identities that hold in the quasivariety, while the filter of left ideals
encodes the quasiidentities. The filter of left ideals defines a generalized
notion of torsion.
  It follows from our result that if $R$ is left Artinian, then any relatively
congruence modular quasivariety of left $R$-modules is axiomatizable by a set
of identities together with at most one proper quasiidentity, and if $R$ is a
commutative Artinian ring then any relatively congruence modular quasivariety
of left $R$-modules is a variety.
