In this question I asked: "Are unique prime ideal factorization domains noetherian?".
In this answer Badam Baplan pointed out that locally noetherian domains are unique prime ideal factorization domains (UPIFD), that certain non-noetherian domains are locally noetherian (the first example seems to have been given by N. Nakano in 1953), and thus that these non-noetherian domains are UPIFD.
This prompts the present question:
Are unique prime ideal factorization domains locally noetherian?
Edit. For the sake of completeness recall that a UPIFD is a domain satisfying the following condition:
If $\mathfrak p_1,\dots,\mathfrak p_k$ are distinct nonzero prime ideals of $A$, and if $m$ and $n$ are distinct elements of $\mathbb N^k$, then we have $$ \mathfrak p_1^{m_1}\cdots\mathfrak p_k^{m_k}\ne\mathfrak p_1^{n_1}\cdots\mathfrak p_k^{n_k}. $$
