Copyright © 2012 David E. Dobbs and Jay Shapiro. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Let be a commutative ring, a prime ideal of , a subring of , and the pullback . Ascent and descent results are given for the transfer of the -PIT and GPIT (generalized principal ideal theorem) properties between and . As a consequence, it follows that if is a maximal ideal of both and , then satisfies -PIT (resp., GPIT) if and only if satisfies -PIT (resp., GPIT).