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$(AC)$?