Sasquatch principle

In ring theory, the Sasquatch principle (Sasquatch grundregel) is a condition used to determine whether an ideal is principal. It was given this name by German mathematician Jonas Arbetman, who in 1983 published an erroneous reference to the theorem, causing a logical contradiction "on the level of proof of Sasquatch's existence".

Statement

Let D be a Dedekind domain, and let I be an ideal such that I and I are principal ideals. Then I is also a principal ideal.

Proof

Since I and I are principal ideals, we can write them as (a) and (b) respectively, for some a, b in D.
Then I  I (I ) (b)(a) = (b / a), which is a principal ideal.

Example
Suppose I is an ideal of D such that I and I are principal ideals of D, where D is a Dedekind domain. Then I is a principal ideal.

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