Abstract
It is well known that a finite totally ramified extension of a local field can be generated by a uniformising element the minimal polynomial of which is also Eisenstein. The quadratic and the quartic normal totally ramified extensions of Q 2 are well known and well characterized. In this note we characterize the Eisenstein polynomials of degree 4 with coefficients in Z 2 that define normal totally ramified extensions of Q 2. Furthermore we give some necessary conditions for the cyclic case of degree 2n. Also examples are given.
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Lbekkouri, A. On the construction of normal wildly ramified extensions over Q 2 . Arch. Math. 93, 235–243 (2009). https://doi.org/10.1007/s00013-009-0024-5
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DOI: https://doi.org/10.1007/s00013-009-0024-5