## Every Prime Ideal of a Finite Commutative Ring is Maximal

## Problem 723

Let $R$ be a finite commutative ring with identity $1$. Prove that every prime ideal of $R$ is a maximal ideal of $R$.

Add to solve laterLet $R$ be a finite commutative ring with identity $1$. Prove that every prime ideal of $R$ is a maximal ideal of $R$.

Add to solve later