  Professor Daniel Anderson informed me, recently, that there is an error in
the proof of Theorem 56 of Kaplansky's book on Commutative Rings. His (Dan's)
reason was "He (Kaplansky) orders by reverse inclusion but in the last line
uses inclusion, so we don't contradict maximality (which is minimality)". The
aim of this short note is to indicate that while Dan Anderson appears to be
correct in pointing out an error in the proof of Theorem 56 of the above
mentioned book, the statement of the theorem is a correct consequence of a
Theorem of Chevalley.
