Abstract
A bounded partially ordered set
I is a complemented modular lattice if and only if the semigroup
B(
I) of all strongly range-closed residuated transformations of
I is a regular semigroup coordinatizing
I. If
S is any strongly regular Baer semigroup coordinatizing
I, then the Janowitz representation of
S maps
S homomorphically onto a full regular subsemigroup of
B(
I). It is shown that the Janowitz representation of
S is equivalent to Hall's (or Grillet's) fundamental representation.