We have that, $x^{n}=0$ for some $n$ $\in$ $\mathbb{Z}_{+}^{*}$.
I want to find some $y$ $\in$ $A$, such that, $(x+u)y=1$, so that $(x+u)$ is unity of $A$.
Could you help me determine $y$ or show a better demonstration?
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4Hint: it suffices to show $1 + u^{-1}x$ is a unit. How might we compute $\frac{1}{1+a}$? – Joshua Mundinger Jun 12 '18 at 15:54
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Is $A$ commutative? – Robert Lewis Jun 12 '18 at 16:09
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1Yes, A is commutative. – wavilson ferreira Jun 12 '18 at 16:13