# Finite Ring with Multiplicative Norm is Field

(Redirected from Finite Normed Ring is Field)

## Theorem

Let $R$ be a finite ring with a multiplicative norm.

Then $R$ is a field.

## Proof

From Ring with Multiplicative Norm has No Proper Zero Divisors, $R$ has no proper zero divisors.

From Finite Ring with No Proper Zero Divisors is Field, $R$ is a field.

$\blacksquare$