On conductor overrings of an integral domain (Q802608)

Let R be an integral domain with identity having quotient field K. For an ideal I of R, \(I:_ KI=\{x\in K| xI\subseteq I\}\) is an overring of R contained in the ideal transform T(I). The author shows that the map \(P\to (P\cap I):_ KI\) gives a one-to-one correspondence between the set of all prime ideals P of R not containing I and the set of all prime ideals of \(I:_ KI\) not containing I. Furthermore, with P as above, \(I:_ KI/((P\cap I):_ KI)\) is isomorphic to a subring of \((I+P)/P:_ L(I+P)\) where L is the quotient field of R/P.