Originally Posted by

**rubix** Let me start by saying i have missed pretty much the entire lecture on Group Homomorphism and probably more than a half of Ring Homomorphism so go easy on me.

I'm trying to catch up from the book...trying to do as much exercise as i can but i'm stuck on the very basic idea. How to determine all Group and Ring Homomorphism for a given mapping.

I know the properties of Homomorphism, theorems/lemmas related to it...and atm i can do problems like "given mapping, prove or disprove it is ring homomorphism".

Anyway, how does one go aboot approaching such problems? Am i supposed to use 1-> 1 property, if so how?

Here are some examples:

{ i would really appreciate if you gave a through explanation (along with your approach if possible) rather than just the solution }

1a) Determine all homomorphisms from Z_12 to Z_30

1b) Determine all ring homomorphisms from Z_12 to Z_30

2) Determine all ring homomorphisms from Z/6 to Z/2

3) Determine all ring homomorphisms from Q -> Q

Much appreciated!