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

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.


James Harris

.

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