Maximal Spectrum of Ring is Nonempty

Theorem
Let $A$ be a non-trivial, commutative ring with unity.

Then its maximal spectrum is nonempty:
 * $\operatorname{Max} \operatorname{Spec} \left({A}\right) \ne \varnothing$

Proof
This is a reformulation of Krull's Theorem.

Also see

 * Spectrum of Ring is Nonempty