Transfer of the GPIT Property in Pullbacks

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).