Question 35
Let $(A,+, \cdot)$ be a commutative ring (with identity) and let $U(A)$ be the set of invertible elements of the ring.
a) If $x \in A$ and $x^{2}=0$, show that $1+x \in U(A)$.
b) Let $x \in A$ for which there exists $n \in \mathbb{N}^*$ such that $x^{n}=0$, and let $u \in U(A)$. Show that $u+x \in U(A)$.
a) If $x \in A$ and $x^{2}=0$, show that $1+x \in U(A)$.
b) Let $x \in A$ for which there exists $n \in \mathbb{N}^*$ such that $x^{n}=0$, and let $u \in U(A)$. Show that $u+x \in U(A)$.