Geodesic
On the structure of two-dimensional local skew fields
Izvestiya. Mathematics , Tome 65 (2001) no. 1, pp. 23-55

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The concept of $n$-dimensional local skew field is a direct generalization of the concept of $n$-dimensional local field. We study 2-dimensional local skew fields and solve the classification problem for the those of characteristic 0 whose last residue field is contained in the centre, and suggest a condition under which there is a section of the residue map whose first residue skew field is commutative. Under this condition we solve the classification problem for all 2-dimensional local skew fields. For skew fields of characteristic 0 whose last residue field is contained in the centre, we state a criterion for two elements to be conjugate. 
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     title = {On the structure of two-dimensional local skew fields},
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A. B. Zheglov. On the structure of two-dimensional local skew fields. Izvestiya. Mathematics , Tome 65 (2001) no. 1, pp. 23-55. http://geodesic.mathdoc.fr/item/IM2_2001_65_1_a1/