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

[William Hughes, to JSH]
Have you still not understood that for the algebraic integers

-if a and b are coprime they remain coprime in any
ring that contains the algebraic integers.

No, the algebraic integers are not like the evens. If something
is coprime in the algebraic integers it stays coprime.

[The converse is not true. If a and b are not coprime in the algebraic
integers it is trivial to find a ring containing the algebraic integers
in which a and b are coprime]

I expect it's a mistake to assume that James knows what mathematicians mean
when they say two elements of a ring are coprime, except (and only except)
when the ring is Z. In the case of Z, he understands a consequence of the
general ring definition as it happens to work out in Z (hardly an accident,
since the general definition is a generalization of what happens to be true
in Z ...), but I bet he isn't even aware of the general definition. Even if
he is, he certainly doesn't know how to apply it.

Think about it ;-) Has he ever said something demonstrating the slightest
idea of what an ideal is, apart from mechanically repeating that he's proved
ideal theory wrong -- and even then, only after someone else gave him the
phrase "ideal theory" to begin with?

For that matter, I expect it's a mistake even to assume that James
understands what "ring" means. One reason he can't follow obvious
refutations of his goofiest claims appears to be that he literally can't
comprehend what he's reading: if it's concise & accurate, he dismisses at
once as "math-ese", but if it's "folksy" he automatically substitutes in his
own private (& hopelessly careless) meanings for technical phrases. Ask him
to define one of his terms -- his "definition" of "the object ring" is one
of his /better/ <brrrr> efforts of that kind.

Oblique thanks to J K Haugland for fixing this URL:

http://en.wikipedia.org/wiki/Crank_%28person%29

...
Cranks who contradict some mainstream opinion in some highly technical
field, such as mathematics or physics, almost always

1. exhibit a marked lack of technical ability,

2. misunderstand or fail to use standard notation and terminology,

3. ignore fine distinctions which are essential to correctly
understanding mainstream belief.

#2 and #3 pervade most attempts to discuss a tech issue with JSH.


.

Relevant Pages

  • 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)
  • Re: JSH: The "Published" paper he dosent what you to know about.
    ... -if a and b are coprime they remain coprime in any ... ring that contains the algebraic integers. ... the algebraic integers are not like the evens. ... I expect it's a mistake to assume that James knows what mathematicians mean ...
    (sci.math)