I have to prove Y: Z -> Zm defined by Y(x) = [x] is a homomorphism, but I don't remember what [x] means. Any help would be greatly appreciated! Thanks!

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- March 21st 2010, 12:15 PM #1

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- March 21st 2010, 01:08 PM #2

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Ok, I figured out [x] (it's the congruence class of x, yay!), but I'm given that the mapping in my first post is a homomorphism and I'm told to prove it. In order to prove that, I would have to show [x + y] = [x] + [y].

I don't see how that is true; for mod 3, [0] = {..., -6, -3, 0, 3, 6, ...} and

[1] = {..., -5, -2, 1, 4, 7, ...}. According to that equation, [0 + 1] = [0] + [1] = {..., -11, -5, 1, 7, 13, ...} which would be [1] with respect to mod 6.

Am I on the right track here, or am I completely off?

- March 22nd 2010, 01:30 PM #3

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- March 22nd 2010, 08:08 PM #4