Summary: Let \(T\) be a commutative ring, \(I\) a prime ideal of \(T, D\) a subring of \(T/I\), and \(R\) the pullback \(T\times_{T/I}D\). Ascent and descent results are given for the transfer of the \(n\)-PIT and GPIT (generalized principal ideal theorem) properties between \(T\) and \(R\). As a consequence, it follows that if \(I\) is a maximal ideal of both \(T\) and \(R\), then \(R\) satisfies \(n\)-PIT (resp., GPIT) if and only if \(T\) satisfies \(n\)-PIT (resp., GPIT).