We define below a notion for modules which is dual to that of faithful, and a notion of “fully
divisible” which generalizes that of injectivity. We show that the bicommutator of a cofaithful,
fully divisible left R-module is isomorphic to a subring of Qmax (R), the complete ring of left
quotients of R. In recent papers, Goldman [2] and Lambek [3] investigated rings of left
quotients of a ring R constructed with respect to torsion radicals. It is known that every ring of
left quotients of R is isomorphic to the bicommutator of an appropriate injective left R …

It has been pointed out to me by EA Rutter that Proposition 2.4 (i) is incorrect in that the proof
does not establish the uniqueness of the QM (R)-module structure defined on RN.(Notation
is that of the original paper.) It is true that N is a QM (ft)-module under the multiplication
defined for all q G QM (R) and n£ N by qn=</> n (g), where< t> n: I—» N is any extension of
[r>-> rn]= fn: ft—> N to I instead of just to QM (R)-Note that if< j> n and< t> nf both extend/w,
then they agree on\JM (R). This might be called the QM (R)-module structure induced on N …