\(R\) denotes an associative ring with identity and all modules are right unital. Finitely generated projective modules (\(\text{FP}(R)\)) over an exchange ring \(R\) are studied first and it is shown that a module \(P\) is isomorphic to a direct summand of a module \(Q\) (resp. \(P\simeq Q\)) if and only if \(P/PI\) is isomorphic to a direct summand of \(Q/QI\) (resp. \(P/PI\simeq Q/QI\)) for any ideal \(I\) of \(R\) such that \(R/I\) is indecomposable and \(J\)-semisimple.
On the other hand, if \(R/J(R)\) is an exchange ring, then the cancellation law holds in \(\text{FP}(R)\) if and only if the cancellation law holds in \(\text{FP}(R/I)\) for any ideal \(I\) of \(R\) such that \(R/I\) is indecomposable and \(J\)-semisimple.
Properties of exchange rings \(R\) are studied next and results with respect to the unit 1-stable range condition and idempotents of \(R\) are obtained.