Quotient Rings and Homomorphisms

  • #1

Homework Statement

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.

Homework Equations

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?
  • #2
You need to review your definitions of ring homomorphism and surjective function. Neither one that you gave is accurate.

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