Thread: Homomorphism

Prove that the map from
pi : (Z; +) -> (Z_n; +)
that takes x to [x]_n is a group homomorphism.


I know what a homomorphism is, not sure how to prove this case...

Originally Posted by CarmineCortez

Prove that the map from
pi : (Z; +) -> (Z_n; +)
that takes x to [x]_n is a group homomorphism.


I know what a homomorphism is, not sure how to prove this case...

Is it true that [z+w]_n = [z]_n + [w]_n? This is the same as asking: is addition modulo n well defined?

Tonio