Maximal Spectrum of Ring is Nonempty

Theorem

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

Then its maximal spectrum is non-empty:

$\operatorname {Max} \Spec A \ne \O$

Proof

This is a reformulation of Krull's Theorem.

$\blacksquare$

Also see

• Spectrum of Ring is Nonempty