On Matlis dualizing modules (Q1608218)

A ring \(R\) has a Matlis dualizing module if there is a faithfully balanced \((R,R)\)-bimodule \(E\) such that \(_RE\) and \(E_R\) are both injective cogenerators. In the reviewer's book `Rings with Morita duality' [Lect. Notes Math. 1523, Springer (1992; Zbl 0790.16009)], this is called a Morita self-duality. The authors prove that the number (whether finite or infinite) of distinct dualizing modules equals the number of distinct invertible \((R,R)\)-bimodules and show by example that this number can be greater than one.