Let A be an artin ring which is also a finitely generated algebra over Z.

Show that |A|<$\infty$

If A would have been a field then I know how to prove it. I know that A is a product of local rings, so I could restrict the question to Local artin rings that are finitely generated algebra over Z. But how does this help?

Thanks, Yatir

Let A be an artin ring which is also a finitely generated algebra over Z.

Show that $|A|<\infty$.

If A would have been a field then I know how to prove it. I know that A is a product of local rings, so I could restrict the question to Local artin rings that are finitely generated algebra over Z. But how does this help?

Thanks, Yatir