Proper Ideal iff Quotient Ring is Nontrivial
Jump to navigation
Jump to search
This theorem requires a proof..
You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof.
Theorem
Let $A$ be a commutative ring.
Let $\mathfrak a \subseteq A$ be an ideal.
The following are equivalent:
- $(1): \quad \mathfrak a$ is a proper ideal
- $(2): \quad$ The quotient ring $A / \mathfrak a$ is nontrivial ring
Proof
You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof.
When this page/section has been completed, {{ProofWanted}} should be removed from the code.
If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page (see the proofread template for usage).
