Re: JSH: Blocking and ring of algebraic integers



JSH wrote:

<snip>

Note then as I now give the correct form that

P(x) = (g_1(x) + 2)*(g_2(x) + 1)

cannot exist in the ring of algebraic integers when P(x) is a
polynomial with integer coefficients, g_1(0) = g_2(0) = 0, and the g's
are not rational with rational x.

Be careful here. Your last two conditions are contradictory, since
if g_i(0) = 0, then g_i(x) will be rational for x = 0.


Regards,

Rick
.



Relevant Pages

  • Re: JSH: Inconsistency with algebraic integers
    ... set of algebraic integers to form a ring or not? ... <snip same old crap> ...
    (sci.math)
  • Re: JSH: Weird but fascinating
    ... true if by "blocked" you mean that no such factorization is ... Notice that we don't even need the ring of algebraic integers here. ...
    (sci.math)
  • Re: JSH:Understanding constant terms
    ... You have imposed demands on the ring of algebraic integers which are ... with no real mathematical importance. ... That requirement defines a perfectly valid ring. ... [snip irrelevant and redundant exposition of fallacious arguments] ...
    (sci.math)
  • Re: JSH: Simpler explanation important as to motive
    ... factor in the ring of integers -- but is stated in a much messier ... is not the ring of algebraic integers - even he would agree ... I don't think that's what Harris had in mind ... ...
    (sci.math)
  • Re: My paper, and the cheaters
    ... What ring *are* you working in? ... > The paper starts in the ring of algebraic integers and proceeds by ... The only possible reason, obviously, is that you used some reasoning ...
    (sci.math)