Re: JSH: The "Published" paper he dosen't what you to know about.

marcus_b wrote:
jst...@xxxxxxx wrote:
marcus_b wrote:
jstevh@xxxxxxx wrote:
marcus_b wrote:

<deleted>

One of the simpler cases to which your result should
apply is when f = sqrt(5). In that case, the polynomial
equation above becomes

a^3 + 12 a^2 - 65 = 0.

This is a monic polynomial with integer coefficients.
It is irreducible over the rationals. The roots
are algebraic integers. Dedekind's theorem
and Galois theory both say that none of the roots are
coprime to f^2 = 5 in the ring of algebraic integers.
You however infer that one of the roots IS coprime
to 5. And since you are saying that Galois theory is
wrong, you must be saying that it is wrong in the ring
to which it applies: the ring of algebraic integers.
From which we must conclude: you think one of roots is
coprime to 5 *** in the ring of algebraic integers.***
This is inescapable.


Nope.

Why go in circles? I already note that the result isn't true in the
ring of algebraic integers, so why come back and claim that I'm saying
it's true in the ring of algebraic integers?

It's trivial math too.

You're doing what other posters have tried to do which is claim I'm
saying what I'm not, and denying the reality that I acknowledge that
none of the roots can be coprime to 5 in the ring of algebraic
integers.


Your paper says Galois theory disagrees with your algebra.
The Galois theory in question applies to the ring of algebraic
integers, not to arbitrary rings. Therefore you must be saying
that your results - particularly your claim that one of a1(m),
a2(m) or a3(m) is coprime to f - must apply in the ring of
algebraic integers. Otherwise you have no reason to say
Galois theory is incorrect.

Marcus.


It's false implication.

One can correctly say that 2 is coprime to 6 in evens, right?

But what if some mathematician proclaims that means that 2 is coprime
to 6 in a larger sense?

No one would, of course, because you know that 2*3 = 6.


As you well know, this is irrelevant. The rigorous definition
of coprimeness applies only to rings with a multiplicative
identity. The ring of even numbers is not such a ring.


A telling dodge as the analogy explains quite simply what the coverage
problem with the ring of algebraic integers is.



But what I've done is prove a similiar situation where it's not so
trivial to point to the error, so mathematicians who if they admit the
error have no accomplishments in their entire careers can dance around
the proper conclusion.

So that means that Galois Theory doesn't say anything differently for
non-rationals than it does for rationals as the ring of algebraic
integers is irrelevant.

The ring of algebraic integers is a historical oddity, with no
mathematical importance.


I'll try this one more time, real simple. You say your algebra
shows that Galois theory is wrong. But the Galois theory result
you think you have contradicted is valid in the ring of algebraic
integers, not necessarily in other rings. If your claimed result is
true in some other ring, then it does not contradict Galois theory
because Galois theory does not apply to that ring.
So you cannot conclude that Galois theory is wrong. But you
DO claim that you have shown Galois theory to be wrong.
Therefore you must have concluded somehow that your result
applies to the domain of validity of Galois theory, i.e., the ring
of algebraic integers.


I never said Galois Theory was wrong. I've said it is wrongly used.

It is ideal theory that is just flat wrong.

The proof is easy.

Now readers consider that dead journal one more time.

You know they published my paper, retracted it, and then managed one
more edition before just shutting down the journal.

Did it occur to any of you that they shut down when they realized
beyond any doubt that my result was right?

I did manage to communicate with at least one of the editors during the
debacle, and what I did was forward him the emails from the Cornell
math grad student who stepped through the argument--thinking he'd find
an error to convince me I was wrong.

Yup, that Cornell math grad student I bring up so much.

I forwarded HIS work to one of the SWJPAM editors.

Did it occur to any of you that the journal shut down as the editors
felt despair realizing I WAS right?


James Harris

.

Relevant Pages

  • Re: JSH: The "Published" paper he dosent what you to know about.
    ... the "Over Iinterpertations of Galois Theory" by mathematicians. ... Determining the distribution of factors within irrational algebraic integers ... one of the a's is coprime to 5. ... that are themselves polynomials. ...
    (sci.math)
  • Re: JSH: The "Published" paper he dosent what you to know about.
    ... I'm not sure what he wants from his "object ring", ... so the other factors needed to be coprime to f --- in the ring ... happen in the ring of algebraic integers. ... Dedekind's work and the theory of ideals. ...
    (sci.math)
  • Re: Attacking my algebraic integer work
    ... > The paper Advanced Polynomial Factorization has been retired. ... >> his arithmetic in the ring of algebraic integers. ... not coprime to 5 in some yet-to-be-well-defined ring of objects, ...
    (sci.math)
  • Re: JSH: Brainstorming over, for now
    ... You requested a proof that one could prove that an algebraic number could be expressed as the quotient of two coprime algebraic integers. ... >> So consider what follows from the ring of algebraic numbers, ... You're right, factorization can be done by infants using ordinary household materials, but we're really save, and the NSA doesn't need to get in on the game? ...
    (sci.math)
  • Re: JSH: The "Published" paper he dosent what you to know about.
    ... are algebraic integers. ... You however infer that one of the roots IS coprime ... And since you are saying that Galois theory is ... you must be saying that it is wrong in the ring ...
    (sci.math)
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