# All questions with tag [math: artinian]

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## Showing a ring is Artinian?

We have a ring $R=\begin{pmatrix} \mathbb{Z} & 0 \\ \mathbb{Z} & \mathbb{Z} \end{pmatrix}$ Let $I=\begin{pmatrix} 12\mathbb{Z} & 0 \\ 3\mathbb{Z} & 3\mathbb{Z} \end{pmatrix}$ How do I show that $R/I$ is Artinian ring? $R/I=I$ , the only perfect that isn't equivalent to I is $\begin{pmatrix} 0 & 0 \\...

2022-06-30 00:42:37