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exceptional units

Source: miklos schweitzer 1993 q3

October 20, 2021
abstract algebrafinite fields

Problem Statement

Let K be the field formed by the addition of a root of the polynomial x4−2x2−1x^4 - 2x^2 - 1 to the rational field. Prove that there are no exceptional units in the ring of integers of K. (A unit ε\varepsilon is called exceptional if 1−ε1-\varepsilon is also a unit.)
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