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


Tim Peters wrote:

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.

I think this has been the problem, or one of them, all along. James
concludes two algebraic integers are coprime, when if you look at his
reasoning that isn't what he ought to be saying. If he'd said of the
three roots of y^3-12*y^2+65=0, one of the roots is a 5-adic unit, then
he would have said something which made sense in terms of the arguments
he was bringing. Instead he says it is coprime to 5, which sends the
whole discussion off in the wrong direction. Moreover, James comes to
this conclusion indirectly, looking at the factorization of the norm
term, and doesn't understand what it is he's really got an example of.

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?

No, and if you look at what he says, ideals play no role in his notion
of coprimality.

.

Relevant Pages

  • 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)
  • 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. ... ideal theory wrong -- and even then, only after someone else gave him the ...
    (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. ... ideal theory wrong -- and even then, only after someone else gave him the ...
    (sci.math)
  • Re: James object ring
    ... >> the other roots are not. ... >> has shown that there is no maximal ring with that property. ... any integers that are coprime in the ring of integers. ... James harris ...
    (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)