From: Peter Freyd <pjf@saul.cis.upenn.edu>
To: baez@math.ucr.edu, categories@mta.ca.barr.anil@math.cornell.edu
Subject: Re: Construction of a real closure
Date: Fri, 5 May 2006 16:34:50 -0400 (EDT) [thread overview]
Message-ID: <24080.986940726$1241019218@news.gmane.org> (raw)
If memory serves me, Nerode proved years ago that the necessary and
sufficient condition that all the algebraic closures of a field are
effectively isomorphic is that its polynomials effectively factor into
irreducibles.
As for the later, the ancient theorem is that if a unique
factorization domain has only finitely many units and if the
factorization is effective then so it is for its polynomial ring.
The condition on units pretty much forces the proof.
next reply other threads:[~2006-05-05 20:34 UTC|newest]
Thread overview: 13+ messages / expand[flat|nested] mbox.gz Atom feed top
2006-05-05 20:34 Peter Freyd [this message]
-- strict thread matches above, loose matches on Subject: below --
2006-05-07 20:28 Marta Bunge
2006-05-06 13:53 Michael Barr
2006-05-06 2:24 Eduardo Dubuc
2006-05-05 14:55 John Baez
2006-05-05 13:45 Peter Freyd
2006-05-05 13:30 Marta Bunge
2006-05-05 12:22 Michael Barr
2006-05-05 2:14 Phil Scott
2006-05-04 23:28 Michael Barr
2006-05-04 22:20 Marta Bunge
2006-05-04 22:20 Marta Bunge
2006-05-04 15:22 Michael Barr
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