For most Integral domains I found that are Not UFD, they just does not have the uniqueness of factorization, while they still possess the existence of factorization. ($\mathbb{Z}[\sqrt{-5}]$ for example)
I searched on Wiki and found that the Uniqueness corresponds to being in a GCD domain, and Existence corresponds to Accending Chain Condition of Principal ideal(ACCP)
So, I am wondering is there any integral domain between the GCD domain & UFD?
