# Power series ring $R[[X_1,\ldots,X_d]]$ over a domain $R$

Let $$R$$ be a domain and \begin{align*} T \,\colon= R[[X_1,\ldots,X_d]]. \end{align*} Suppose that we have $$d$$ elements $$f_1,\ldots,f_d \in T$$ and let us consider an ideal $$J$$ of $$T$$ such that $$(f_1,\ldots,f_d) \subset J$$ and the following three conditions$$\colon$$ \begin{align*} & 1. \quad \overline{f_i} \,\colon \overset{{\mathrm{def}}}{=} f_i~{\mathrm{mod}}(X_1,\ldots,X_d)~{\mathrm{is~ an~ irreducible~ element~ of~}} R ~{\mathrm{for~each}}~ 1 \leq i \leq d. \\ & 2. \quad T/(f_1,\ldots,f_d) \phantom{a} {\mathrm{is}}~not~{\mathrm{finite~over}}~ R. \\ & 3. \quad T/J \phantom{a} {\mathrm{is~finite~over}}~R. \end{align*}