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 RingPlease assess the validity of this proposal. (discuss)
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.
By Quotient Ring of Ring with Unity is Ring with Unity, $R / J$ is a ring with unity.