Transfer of the GPIT Property in Pullbacks

Abstract EN

Let T be a commutative ring, I a prime ideal of T, D a subring of T/I, and R the pullback T×T/ID.

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).