Upgrade to access all content for this subject

Let $R$ be a nonzero commutative ring with identity $1_R$.

Which of the following properties can $R$ share with $\mathbb{Z}/12\mathbb{Z}$ and still be an integral domain?

There exist $r,s\in R\setminus\{0\}$ with $rs=0$.

$R$ is isomorphic to a product of $2$ nonzero rings.

The set of units of $R$ is strictly contained in $R\setminus\{0\}$.

The characteristic of $R$ is not a prime number.