Possible Duplicates:

Is the statement that every field has an algebraic closure known to be equivalent to the ultrafilter lemma?

algebraic closure of commuting pairs of matrices

we need **zorn's lemma** for proving that every field $F$ has a **unique algebraic closure**. but I haven't seen a converse for this important Theorem.

From the above illustration my question is:

Is it true that the existence of The unique algebraic closure is equevalent to *

axiom of choice*$(AC)$?