Re: Embedding Boolean Algebras

From: William Elliot (marsh_at_privacy.net)
Date: 11/02/04 

Date: Tue, 2 Nov 2004 02:24:49 -0800

On Mon, 1 Nov 2004, Noel Vaillant wrote:

> [William Elliot]
> > If Krull's theorem applies, it doesn't apply directly.
>
> [Todd Trimble]
> "But the fact that you seem to know something about Boolean algebras
> suggests to me that you *are* aware of this equivalence, and were just
> playing game and/or dodging the issue. That would not be inconsistent with
> the rude tone of your reply. In any case, maybe it's time that you present
> in more detail why Vaillant was wrong about existence of maximal ideals
> (keeping in mind the equivalence noted above), or else just admit that you
> made a mistake. We all do sometimes."
>
That quote from Todd has neither shown up on my browser nor at Google.
Ok, it showed up at mathforum.org. The point now however is mute, for I
took your lead to produce the dual proof using filters (an idea sparked by
Todd's discussion) instead of order-ideals while at the same time
acknowledging you as the orginator of the interesting proposition for
who's proof I suggested the modification. I even thanked you for bringing
it forth. Have my posts of Nov 1, to you and to Todd (cf snip below)
arrived belatedly?

Ok, I see two posts by Todd have arrived at mathforum.org but not yet on
my newserver. I will answer them as they arrive thru my newserver. 

--
> I also think William should stop playing games and acknowledge his mistake.
> Mathematical  discussions are rather pointless otherwise.
From: William Elliot <marsh@privacy.net> Nov 1, 2004
> From: Todd Trimble <trimble1@optonline.net>
> >The existence of an atom, gives a coatom which generates a maximal
> >ideal. Conversely in a Boolean algebra, a maximal ideal gives a
> >coatom, hence an atom.
> I don't get this either.  How does a maximal ideal give a coatom?
No, I was thinking about meet prime elements of principal ideals.