# Recent MathOverflow Questions

### examples of MF algebras

Math Overflow Recent Questions - Sun, 03/17/2019 - 14:46

Can anyone show me concrete examples of unital MF algebra and non-unital MF algebra resepctively? Thanks!

### Power series ring $R[[X_1,\ldots,X_d]]$ over a U.F.D. $R$

Math Overflow Recent Questions - Sun, 03/17/2019 - 13:54

Let $R$ be a U.F.D. 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~ a~ prime~ 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*}