  We show that every complemented modular lattice can be converted into a left
residuated lattice where the binary operations of multiplication and residuum
are term operations. The concept of an operator left residuated poset was
introduced by the authors recently. We show that every strongly modular poset
with complementation as well as every strictly modular poset with
complementation can be organized into an operator left residuated poset in such
a way that the corresponding operators M(x,y) and R(x,y) can be expressed by
means of the operators L and U in posets. We describe connections between the
operator left residuation in these posets and the residuation in their lattice
completion. We also present examples of strongly modular and strictly modular
posets.
