Ring satisfying PIT

Pre-origin
Krull's principal ideal theorem, often abbreviated as the PIT, is a statement about a property (condition) that Noetherian rings satisfy. Krull also came up with a class of integral domains, called Krull domains, which satisfy the property.

Origin
A study of rings satisfying PIT was undertaken, for instance, in the paper On the generalized principal ideal theorem and Krull domains by Anderson, Dobbs, Eakin and Heinzer.

Definition with symbols
A commutative unital ring $$R$$ is said to satisfy PIT or satisfy the Principal Ideal Theorem if given $$x \in R$$, and given $$P$$ as a prime ideal minimal amoung the primes containing $$x$$, the codimension of $$P$$ is at most 1.

Stronger properties

 * Noetherian ring:
 * Krull domain
 * Ring satisfying GPIT