proof

[virginiamath]

I was wondering if anyone could help out on the following proofs.

Theorem 2: ø(a,b) = (b,a) is an automorphism of R2 under compontentwise addition.
Let Zn = {0, 1, ....n-1}under addition and multiplication modulo n.

Theorem 3: Zn is a ring for all n E where n stands for the set of natural numbers, i.e., the set {1,2,3....}

Thanks

 

[tkhunny]

You haven't responded to 123456789's questions.

http://math2.org/mmb/thread/36082

You'll have to clarify, preferably on the original reply.

 

[pka]

Where are you having any difficulty with either of these?
They are both just a mindless exercise in using the definitions.
Showing that \(\displaystyle \phi :R^2 \to R^2\) is an isomorphism is straightforward.

For #3, just check each of the ring properties for \(\displaystyle Z_n\)