1. ## need more examples about ring -_-?

- Commutative ring and uncommutative ring which doesn't have unit element
- Ring which has different unit element with its subring's unit element

thank you

2. Originally Posted by GTK X Hunter
$n\mathbb{Z}, \ n > 1,$ for the commutative case and $\left \{ \begin{pmatrix} a & b \\ 0 & 0 \end{pmatrix}: \ a,b \in \mathbb{R} \right \}$ for the noncommutative case.
$M_2(\mathbb{R})$ and the subring $\left \{\begin{pmatrix}a & 0 \\ 0 & 0 \end{pmatrix}: \ a \in \mathbb{R} \right \}.$
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