Zuo En Lemma is named after mathematician Max Zuo En.

Specifically, suppose

Zon lemma, well-ordered theorem and axiom of choice are equivalent. On the basis of zermelo-Frankel axiom of set theory, the other two can be derived from any of the above three. Zuo En lemma plays an important role in all branches of mathematics, such as proving Hahn-Barnach theorem in functional analysis, asserting that any vector space must have a base, Tychonoff theorem in topology proving that the product space of a compact space is still a compact space, and proving in abstract algebra that any ring must have a maximum ideal and any field must have an algebraic closure.

A typical application of Zon Lemma is to prove any ring.

In order to apply Zon's lemma, it is necessary to prove that

Now consider the core part of the proof: using

In this way, by using Zon lemma,