- #1

- 96

- 0

**Z**is

__not__isomorphic to

**2Z**and that

**2Z**is

__not__isomorphic to

**3Z**. I need now to generalize this. Thus, to prove that rings

**kZ**and

**lZ**, where l≠k are not isomorphic, I need to define an arbitrary isomorphism, and reach a contradiction. So here's what I am thinking. I let f:

**kZ**->

**lZ**be a isomorphism. Then, f(k)=ln , where n is some integer. This is true since k in

**kZ**has to go to

*some*multiple of l. From here, I have just been tinkering around trying to get k to map to 0 so that f is not injective. This worked for the first two. Is this the right approach? Not really looking for a hint, but just an "okay" to keep trying working with this line of reasoning.