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Topic: FLT Discussion: Simplifying
Replies: 65   Last Post: Mar 17, 2001 11:59 PM

 Messages: [ Previous | Next ]
 Peter Percival Posts: 188 Registered: 12/13/04
Re: FLT Discussion: Simplifying
Posted: Jan 18, 2001 7:57 PM

jstevh@my-deja.com wrote:
>
> In article <942neb\$dd5\$1@nntp.Stanford.EDU>,
> Michael Hochster <michael@rgmiller.Stanford.EDU> wrote:

> >
> >
> > : (Sort of like if AB = 0, A or B = 0. These people are saying that

> must
> > : be proven, and that it is a "gap" in my proof that I don't do so.)
> >
> > : If so, I'd like them to say that is their position here and we can

> see
> > : if we can't work that one out.
> >
> > Yes, that is my position. I would like an explanation of why
> > it is true that if AB = 0, then A = 0 or B = 0. I grant that
> > this statement is true when A and B are integers. However,
> > I would like you to verify it when A and B are funny things
> > like x + sqrt(-1)y and x - sqrt(-1)y (x, y integers).
> >

>
> Hey, I've already seen the post where someone says you guys proved that
> AB = 0, when A = 0, or B = 0 by using x^2 + y^2 = 0.
>
> I concede that one could debate the question of whether or not there
> might exist some objects in an infinite ring that could be nonzero and
> multiply times each other to give 0. After all, it's trivally done in
> a finite ring.
>
> So, to me it's become a moot point. Maybe one of you will come back
> with some numbers like quarternions or something where that's not true,
> but hey, I don't mind that as I'd simply find that interesting, and
> worth thinking about whether or not I could work around that.

Are you asking for an example of a ring on an infinite set in which fg =
0 doesn't imply f = 0 or g = 0? Consider the real functions on [0, 1]
(e.g., many other examples can be used). Define (fg)(x) = f(x)g(x) and
(f + g)(x) = f(x) + g(x). Define the ring zero as the constant function
0. Etc.

>
> So, bring it on.
>
> James Harris
>
> Sent via Deja.com
> http://www.deja.com/

--
peter dot percival at cwcom dot net

Date Subject Author
1/15/01 jstevh@my-deja.com
1/15/01 Dik T. Winter
1/16/01 Charles H. Giffen
1/16/01 jstevh@my-deja.com
1/16/01 Randy Poe
1/18/01 jstevh@my-deja.com
1/18/01 Michael Hochster
1/18/01 Peter Johnston
1/18/01 Randy Poe
1/18/01 Doug Norris
1/16/01 Doug Norris
1/16/01 Randy Poe
1/16/01 Dik T. Winter
1/18/01 jstevh@my-deja.com
1/19/01 Dik T. Winter
1/19/01 Randy Poe
1/20/01 jstevh@my-deja.com
1/20/01 oooF
1/21/01 hale@mailhost.tcs.tulane.edu
1/21/01 Peter Percival
1/21/01 Randy Poe
1/26/01 Franz Fritsche
1/19/01 gus gassmann
1/20/01 jstevh@my-deja.com
1/20/01 Doug Norris
1/26/01 Franz Fritsche
1/16/01 hale@mailhost.tcs.tulane.edu
1/16/01 Randy Poe
1/17/01 hale@mailhost.tcs.tulane.edu
1/18/01 jstevh@my-deja.com
1/19/01 hale@mailhost.tcs.tulane.edu
1/20/01 jstevh@my-deja.com
1/21/01 hale@mailhost.tcs.tulane.edu
1/18/01 Peter Percival
1/19/01 hale@mailhost.tcs.tulane.edu
3/17/01 Ross A. Finlayson
1/16/01 hale@mailhost.tcs.tulane.edu
1/18/01 jstevh@my-deja.com
1/19/01 hale@mailhost.tcs.tulane.edu
1/29/01 jstevh@my-deja.com
1/19/01 Dik T. Winter
1/21/01 Dennis Eriksson
1/15/01 Michael Hochster
1/16/01 jstevh@my-deja.com
1/16/01 Michael Hochster
1/18/01 jstevh@my-deja.com
1/18/01 Peter Percival
1/18/01 Randy Poe
1/19/01 oooF
1/21/01 Dik T. Winter
1/21/01 oooF
1/18/01 Edward Carter
1/19/01 W. Dale Hall
1/19/01 Michael Hochster
1/16/01 Randy Poe
1/16/01 Randy Poe
1/17/01 W. Dale Hall
1/17/01 W. Dale Hall
1/19/01 oooF
1/16/01 Charles H. Giffen
1/16/01 David Bernier
1/16/01 jstevh@my-deja.com
1/18/01 Arthur
1/30/01 plofap@my-deja.com
1/30/01 plofap@my-deja.com
1/30/01 plofap@my-deja.com