Solution
= Solution
If $b^k=0$, then $(u+b)^{-1}=u^{-1}\sum_{j=0}^{k-1}(-bu^{-1})^j$. For the <polynomial>, its positive-degree part is nilpotent by (ii), so adding it to the unit $a_0$ gives a unit.
= Solution
If $b^k=0$, then $(u+b)^{-1}=u^{-1}\sum_{j=0}^{k-1}(-bu^{-1})^j$. For the <polynomial>, its positive-degree part is nilpotent by (ii), so adding it to the unit $a_0$ gives a unit.