[FOM] "Mathematician in the street" on AC

[Rupert McCallum]

-----Original Message-----
From: fom-bounces at cs.nyu.edu [mailto:fom-bounces at cs.nyu.edu] On Behalf Of Daniel Méhkeri
Sent: Friday, 21 August 2009 5:01 AM
To: fom at cs.nyu.edu
Subject: [FOM] "Mathematician in the street" on AC

> I guess there are loads of examples where weaker versions goes by without comment even where care is being
> taken to point out full AC.

One example of this is in D. J. H. Garling's textbook "Galois Theory" where he is clearly attempting to signal every use of AC (as with the proof that every proper ideal in a commutative ring is contained in a maximal ideal, or that every field has an algebraic closure) but he fails to signal the use of DC when proving the assertion that in a Noetherian commutative ring every proper principal ideal is contained in a maximal proper principal ideal.