Generalized abc conjecture over number fields

Let $K$ be a number field and let $I$ be an ideal of $\mathcal{O}_K$. Define

$$\operatorname{Rad}(I):=\prod_{\mathfrak{p}\mid I}N(\mathfrak{p}),$$

where $N(\mathfrak{p})=\#(\mathcal{O}_K/\mathfrak{p}\mathcal{O}_K)$. Generalized abc conjecture. For every $\epsilon>0$, there is a constant $C_{K,\epsilon}>0$ such that

$$\prod_v\max\{|a|_v,|b|_v,|c|_v\}\leq C_{K,\epsilon}\operatorname{Rad}(abc)^{1+\epsilon}$$

for all nonzero $a,b,c\in\mathcal{O}_K$ satisfying $a+b=c$. This is a number-field form of the abc conjecture and is cited in the source in connection with Gras's conjecture; its status is open.