- #1

ArcanaNoir

- 772

- 4

## Homework Statement

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]

## Homework 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.

## 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+

[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.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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