A Construction for Absolute Values in Polynomial Rings
نویسنده
چکیده
‖b+ c‖ ≤ max (‖b‖, ‖c‖) then the value ‖b‖ is called non-archimedean. The thus delimited nonarchimedean values are of considerable arithmetic interest. They are useful in questions of divisibility and irreducibility and in fact often correspond exactly to the prime ideals of the given ring. This paper is devoted to the explicit construction of non-archimedean values. More specifically, given all such values for the field R of rational numbers, we construct all possible values of the ring R[x] of all polynomials in x with coefficients in R.
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