  The set of idempotents of a regular semigroup is given an abstract
characterization as a regular biordered set in [2], and in [4] it is shown how
a biordered set can be associated with a complemented modular lattice. Von
Neumann has shown earlier that any complemented modular lattice of order
greater than 3 can be realized as the lattice of principal right ideals of a
regular ring (see [3]). Here we try to connect these ideas to get a
characterization of the biordered sets of a class of regular rings.
