Thread: ring homomorphism

Show that the map f : Z9 maps to Z12 defined as x maps to 4x is a well defined ring
homomorphism. What is the kernel of this map. Find the quotient ring and
give it's multiplication table.

Well definition: Just check if, whenever x = y then Pretty straightforward
Kernel: What such 4x is divisible by 12, Ker = {0, 3, 6}
Quotient Ring: so 3 elements in the quotient ring.
Multiplication Table

--0 1 2

0 0 0 0

1 0 1 2

2 0 2 1