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From: William Elliot on 27 Jul 2010 23:47
On Mon, 26 Jul 2010, Saviola wrote:

I suggest you post your question, reorganized as below, at
sci.math.research. At the end, I give my inadequate ideas.

> (BPI): Given a proper ideal J of a boolean lattice B, there exists a
> prime ideal I of B such that I contains J.
>
> (DPI): Given a distributive lattice L, an ideal J of L and a filter F of
> L such that J and F are disjoint, there exists a prime ideal I of L such
> that I contains J and L\I contains F.
>
> Supposedly (BPI) ==> (DPI) can be proved by constructing an embedding
> of a given distributive lattice into a Boolean lattice, to which (BPI)
> is applied.

> (DMI): Every distributive lattice with 1, which has more than one
> element, contains a maximal ideal.

> (AC): Given a non-empty family A={A_i}_(i belongs to I) of non-empty
> sets, there exists a choice function for A.
>
> Similarly, (DMI) ==> (AC) can be proved by applying (DMI) to a suitable
> lattice of sets.

--
Let K be an infinite collection of not empty, pairwise disjoint subsets
of S. Let L be the lattice of subsets of S. Then the ideal generated by
K is a proper ideal. Let I be a maximal ideal containing K.

At this point, in an attempt to conclude an equivalent form
of AxC, I'm puzzled how to use I to create a choice set for K.

----
From: Saviola on 29 Jul 2010 15:57
Can you tell me how to post on math.research?

I get the following message there:

Due to persistent technical errors, the Math Forum has disabled our posting mechanism to this moderated group.

Please post to this group via a newsreader.


I tried contacting whoever runs the website, but I didn't get a reply.

Thanks for everything.
From: Chip Eastham on 29 Jul 2010 20:18
On Jul 29, 7:57 pm, Saviola <dacunha...(a)hotmail.com> wrote:
> Can you tell me how to post on math.research?
>
> I get the following message there:
>
> Due to persistent technical errors, the Math Forum has disabled our posting mechanism to this moderated group.
>
> Please post to this group via a newsreader.
>
> I tried contacting whoever runs the website, but I didn't get a reply.
>
> Thanks for everything.

Have you tried posting from Google Groups?

I've not done this recently, but it worked
in the past (albeit with substantial delay
due to the moderation policy). Go to:

http://groups.google.com

and browse to sci.math.research. Or if you
are impatient, here's a direct link:

http://groups.google.com/group/sci.math.research/topics?lnk=srg&hl=en

You will probably need to create a login for
Google Groups in order to post this way.

regards, chip
From: William Elliot on 30 Jul 2010 00:50
On Thu, 29 Jul 2010, Saviola wrote:

> Can you tell me how to post on math.research?
>
> I get the following message there:
>
> Due to persistent technical errors, the Math Forum has disabled our posting mechanism to this moderated group.
>
> Please post to this group via a newsreader.
>
> I tried contacting whoever runs the website, but I didn't get a reply.

Ask the moderators to post your question by emailing
sci-math-research-request(a)uiuc.edu.
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