GM-conditions and GM-rings. (Q1430475)

Let \(U(R)\) denote the set of units of a ring \(R\). The authors say that \(R\) satisfies the GM-condition if for any \(x,y\in R\), there exists \(u\in U(R)\) such that \(x-u,y-u^{-1}\in U(R)\). The authors investigate GM-conditions and GM-rings, and show that every exchange ring with Artinian primitive factors is a GM-ring.