Let $(A,\mathfrak{m})$ be a local artinian ring. Then the following hold:

1. $spec(A)=$1;;$\{\mathfrak{m}\}$
2. ${\mathcal{N}}_A=\mathfrak{m}$ is 1;;nilpotent
3. $x\in A$ is either a unit or nilpotent
   As an example,

• $\mathbb{Z}/(p^n)$ is local artinian, and so is $k[x]/(f^n)$