Re: Prime Spectrum and Axiom of Choice

On Aug 20, 6:23 pm, quasi <qu...@xxxxxxxx> wrote:

I think you should restate your new conjecture in full.

It's too confusing to try to piece together the various scattered
parts to see what you are now claiming.

quasi

Sorry, I was busy in some other things so I couldnt reply at once..
Ok, sorry for the confusion

The question/conjecture NOW is:

Let R be a reduced commutative unitary ring
For X subset of Spec R, denote as usual I(X) = intersection of all Q
in X .

Is this a characterization for isolated points of Spec R:

-- Begin of Conjecture --
P is an isolated point of Spec R
iff
There exists an X subset of Spec R such that :
----------------------
- I(X)=0
- There exists P_0 in Spec A\{P} with I(X\{P}) is contained in P_0
--------------------------
-- End of Conjecture --

I negated the condition in my original post. Since in my last post in
this thread I showed that P is isolated implies the sufficiency
condition of this conjecture. One asks oneself therefore whether the
necessity of this condition can be proven ( ie. P isolated then prove
there exists an X.....).


Sincerely,
Jose Capco



.

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