Height of prime ideals P[[X]] when P 2 = P

In this paper, we prove that if [Formula: see text] is a nonzero prime ideal of an integral domain [Formula: see text] such that [Formula: see text], then the height of [Formula: see text] is at least [Formula: see text]; that is, there exists a chain of prime ideals of the power series ring [Formula: see text] contained in [Formula: see text] of cardinality at least [Formula: see text]. The result fails if [Formula: see text] is replaced by a ring with zero divisors. Furthermore, the fact that the height of [Formula: see text] is at least [Formula: see text] does not imply that [Formula: see text]. In our previous work, we proved that if [Formula: see text] is a non-SFT prime ideal of a valuation domain [Formula: see text], then the height of [Formula: see text] is at least [Formula: see text]. When [Formula: see text] is a valuation domain, the condition [Formula: see text] is equivalent to [Formula: see text] being non-SFT. Consequently, our result extends our previous work from a valuation domain to an arbitrary integral domain.