In mathematics, and more specifically in ring theory, Krull's theorem, named after Wolfgang Krull, asserts that a nonzero ring[1] has at least one maximal ideal.
The theorem was proved in 1929 by Krull, who used transfinite induction.
The theorem admits a simple proof using Zorn's lemma, and in fact is equivalent to Zorn's lemma,[2] which in turn is equivalent to the axiom of choice.