(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

show that if m, n are relatively prime, that is, greatest common divisor of m and n is 1, then [itex] \mathbb{Z} _mn \approx \mathbb{Z} _m \times \mathbb{Z} _n [/itex]

2. Relevant equations

I need to show that [itex] \theta [/itex] is operation preserving, and I need to show that it is one to one and onto.

3. The attempt at a solution

For theta, [itex] \theta ([a]_{mn} +_{mn}) = \theta ([a+b]_{mn})=([a+b]_m,[a+b]_n)= [/itex]

[itex] ([a]_m+_m,[a]_n+_n)=([a]_m,[a]_n)+([b)_m,_n)= \theta ([a]_{mn}) + \theta (_{mn}) [/itex]

Did I assume anything I shouldn't have there?

I'm going to consult my notes about proving 1-1. going to try the kernel thing.

As for onto, how do I show that?

I'm concerned that I haven't used the fact that m, n are relatively prime.

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# Gcd(m, n)=1 implies Zmn isomph to Zm x Zn

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