Ring Homomorphism

A function $f:R\to S$ between Rings is a ring homomorphism if

• $f(x+y)=f(x)+f(y)$
• $f(1)=1$
• $f(x*y)=f(x)*f(y)$

Properties

• $f(0)=0$ and $f(-x)=-f(x)$

  This follows from the usual argument for Group Homomorphisms: