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arXiv · 1406.7529

Joubert's theorem fails in characteristic 2

Zinovy Reichstein
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Abstract

Let L/K be a separable field extension of degree 6. An 1867 theorem of P. Joubert asserts that if char(K) is different from 2 then L is generated over K by an element whose minimal polynomial is of the form t^6 + a t^4 + b t^2 + ct + d for some a, b, c, d in K. We show that this theorem fails in characteristic 2.

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Zinovy Reichstein. 2014-06-29. Joubert's theorem fails in characteristic 2. https://arxiv.org/abs/1406.7529

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