A cancellation theorem for ideals (Q1582738)

A basic theme in commutative ring theory is the cancellation of ideals: Given ideals \(I,J,K\) in a commutative ring \(R\), does \(IK=JK\) imply \(I=J\)? In this paper, the author gives a cancellation theorem for special ideals \(I\) and \(J\) in a Gorenstein local ring. This cancellation theorem has several corollaries dealing with the integral closure of powers of an ideal, reduction numbers, and the syzygetic property.