# Maximal Ideal iff Quotient Ring is Division Ring

This article has been proposed for deletion. In particular: This theorem is not correct. See Discussion page. The correct theorem is Maximal Left and Right Ideal iff Quotient Ring is Division Ring |

## Theorem

Let $R$ be a ring with unity.

Let $J$ be an ideal of $R$.

The following are equivalent:

- $(1): \quad$ $J$ is a maximal ideal.

- $(2): \quad$ The quotient ring $R / J$ is a division ring.

## Proof

By Quotient Ring of Ring with Unity is Ring with Unity, $R / J$ is a ring with unity.