Re: James' object ring

From: fishfry (BLOCKSPAMfishfry_at_your-mailbox.com)
Date: 10/16/04 

Date: Sat, 16 Oct 2004 21:17:47 GMT

In article <3c65f87.0410161124.e8fd8c6@posting.google.com>,
 jstevh@msn.com (James Harris) wrote:

> rupertmccallum@yahoo.com (Rupert) wrote in message
> news:<d6af759.0410141638.328dd707@posting.google.com>...
> > "*** T. Winter" <***.Winter@cwi.nl> wrote in message
> > news:<I5KLIo.FxH@cwi.nl>...
> > > In article <d6af759.0410131920.5d988b2e@posting.google.com>
> > > rupertmccallum@yahoo.com (Rupert) writes:
> > > > James' object ring is a proper over-ring of the algebraic integers
> > > > whose intersection with Q is Z.
> > >
> > > And it should also be a subring of the algebraic nnumbers (although James
> > > does not state that explicitly). Actually what James wants is that for
> > > some irreducible primitive non-monic polynomial (a_n.x^n + ... + a_0)
> > > the inverse of at some of the roots are in the ring and the inverse of
> > > the other roots are not.
> > >
> > > > I was wondering if anyone has a proof that there exist such rings.
> > >
> > > Keith Ramsay has shown that such rings do exist indeed. But he also
> > > has shown that there is no maximal ring with that property.
> >
> > How can that be? Surely by Zorn's lemma there must exist maximal rings
> > with the property.
> >
>
> It turns out that the story here is *really* old as years back I
> started talking about "flat rings" which drew a lot of derision on
> sci.math

If you were to start talking about flat rings again, rest assured that
the subject would still draw the same amount of well-deserved derision.

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