# Ring with Unity has Prime Ideal

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## Theorem

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

Then $A$ has a prime ideal.

## Proof

By Krull's Theorem, $A$ has a maximal ideal.

By Maximal Ideal of Commutative and Unitary Ring is Prime Ideal, $A$ has a prime ideal.

$\blacksquare$