Re: JSH: Stop being dense


Tim Peters wrote:


As best I can make out, the only specific result
of Dedekind's you ever objected to here was this one (which he did indeed
prove using the theory of ideals):

Given algebraic integers a and b, and given that a and b are
coprime in the algebraic integers, there exist algebraic integers
a' and b' such that

a*a' + b*b' = 1

Is that the result you challenge? If so, why do you challenge it? Or if
not, what /are/ you talking about?



This hardly deserves to be called a "result"; it's an immediate
consequence
of the definition. The only thing you need to use ideal theory for is
to
define "coprime" in the first place.

.

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. ... ideal theory wrong -- and even then, only after someone else gave him the ...
    (sci.math)
  • Re: JSH: Stop being dense
    ... Tim Peters wrote: ... Given algebraic integers a and b, and given that a and b are ... The only thing you need to use ideal theory for is ... define "coprime" in the first place. ...
    (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: 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.
    ... 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)