Definition:Isomorphism (Abstract Algebra)/Ring Isomorphism

Definition
Let $\struct {R, +, \circ}$ and $\struct {S, \oplus, *}$ be rings.

Let $\phi: R \to S$ be a (ring) homomorphism.

Then $\phi$ is a ring isomorphism $\phi$ is a bijection. That is, $\phi$ is a ring isomorphism $\phi$ is both a monomorphism and an epimorphism.

Also see

 * Definition:Isomorphism (Abstract Algebra)