Thank you very much!
My problem is:
If $R$ is a commutative ring with identity, and $a, b$ are its elements that are divisible by each other, is it true that they must be associates?
Here, $a$ being divisible by $b$ means there exists an $r \in R$, such that $a=rb$; and $a$ and $b$ being associates means there exists an invertible element $u \in R$ such that $a=ub$.
I was told that this not always true. But I encountered some difficulties in finding a counterexample.