I perceive that not all people here believe the negative primes (-2, -3, -5 and so on). But in number-theoretical sense, they are as good as the positive primes, since both have exactly same divisibily properties. And ideal-theoretically, p and -p generate the same principal ideal, as always do the associates. In the other algebraic number fields than Q we, in fact, can not say that some of the associated primes is "better" or "more correct" than some else.
The (rational) prime defined in PM may be negative equally as positive.
Jussi |
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