Ideals of ring and isomorphic ring :)

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December 23rd 2009, 09:19 AM
GTK X Hunter

Ideals of ring and isomorphic ring :)

1) Find all ideals $N$ of $\mathbb{Z}_{12}$ . In each case compute $\mathbb{Z}_{12}/N$ ; that is, find a known ring to which the quotient ring is isomorphic.

2) Give addition and multiplication tables for $2\mathbb{Z}/8\mathbb{Z}$ . Are $2\mathbb{Z}/8\mathbb{Z}$ and $\mathbb{Z}_4$ isomorphic rings?
December 24th 2009, 03:23 AM
HallsofIvy

Okay, have you tried this at all yourself? Since $Z_{12}$ is commutative, it should be easy. What is the difference between " $Z_2$ " and " $2Z$ "?

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