This post is a notice to the math community.  I do not plan on looking
at replies nor do I plan on replying further in this thread.

The current definition for algebraic integers is flawed in that it
does not provide a complete ring.

That definition depends on a polynomial P(x) of degree n with integer
coefficients being monic so that you have

       P(x) = (x + a_1)...(x + a_n)

but that is unbalanced as a complete ring must handle all non monic
polynomials of degree n with integer coefficients to get

       P(x) = (a_1 x + b_1)...(a_n x + b_n)

but in fact the a's and b's cannot here always be algebraic integers
as I've shown in my paper "Advanced Polynomial Factorization" which
can be found at

  http://groups.msn.com/AmateurMath

which shows the limitations of the current definition.

Universities are hereby enjoined to NO LONGER teach the mathematics
that has been proven false.  Failure to update their curriculum will
be an act of fraud, and universities may face civil liabilities if
they do continue teach it.

As an interim plan given the time frame, I would think that
universities may defer teaching certain mathematics, but I'd suggest
they find a better solution.


James Harris