Existence of minimal primes over a proper ideal
= Existence of minimal primes over a proper ideal
{title2=$\operatorname{Min}_R(I)\neq\varnothing$}
Every proper <ideal> of a unital commutative <ring> is contained in a minimal prime over that <ideal>. A <maximal ideal> supplies a prime containing it, and an intersection of a decreasing chain of primes is still prime. <Zorn's lemma>, with reverse inclusion, therefore supplies a minimal member. No <Noetherian> assumption is needed.