## Every Integral Domain Artinian Ring is a Field

## Problem 437

Let $R$ be a ring with $1$. Suppose that $R$ is an integral domain and an Artinian ring.

Prove that $R$ is a field.

Let $R$ be a ring with $1$. Suppose that $R$ is an integral domain and an Artinian ring.

Prove that $R$ is a field.