Let R and S be rings. Show that [tex]\pi[/tex]:RxS->R given by [tex]\pi[/tex](r,s)=r is a surjective homomorphism whose kernel is isomorphic to S.
The Attempt at a Solution
To show that [tex]\pi[/tex] is a homomorphism map, I need to show that it's closed under addition and multiplication. And to show that it's surjective, I need to show for every x in RxS, f(x)=y for y in R. What does it mean when the kernel is isomorphic to S?