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- Units and Nilpotents 4 answers
Suppose $a^4=0$, for some $a \in R[x]/(d)R[x]$, then prove that $1-a$ is invertible.
I was thinking since $a^4 = a \cdot a \cdot a \cdot a=0$, this implies that $a$ has to be zero (?) . Now we have that $1-a=1-0=1$, and $1$ is invertible, since $1 \cdot 1 = 1$. Is it really that simple or am I making a logical error somewhere?