Re: JSH: Stop being dense

[jstevh@xxxxxxx]
So why would people known as top number theorists around the world NOT
admit the coverage problem with algebraic integers?

What is "the coverage problem", exactly? If you haven't noticed, nodody
knows what you think "the problem" /is/. Is it possible to state what "the
problem" is in mathematical language? "Coverage problem" isn't standard
terminology, so you need to define what it means, or continue to be
misunderstood by everyone.

...
Dedekind in saying that he proved a result that was key in convincing
others that the algebraic integers did give full coverage, said he used
ideal theory, which at that time was a relatively new idea.

Specifically which result are you talking about, and specifically what about
that result is incorrect? 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?

...


.

Relevant Pages

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  • Re: Proving is the easy part
    ... coverage problem of the ring of algebraic integers. ... mathematics after all is just basic algebra. ...
    (sci.math)
  • Re: JSH: Stop being dense
    ... admit the coverage problem with algebraic integers? ... yanking expert status from so many people over that time, and to admit ... others that the algebraic integers did give full coverage, ... Mathematics is crucial for our continued development and "pure math" ...
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  • Re: JSH: Stop being dense
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