Starting from Hensel’s generating set of principal units, we construct a basis of the module of principal units in the multiplicative group of a complete discrete valuation field with a residue field of prime characteristics. The uniqueness of the above basis is proved, as well as the uniqueness of the canonical Shafarevich basis.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 394, 2011, pp. 174-193.
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Vostokov, S. The Hensel-Shafarevich canonical basis in complete discrete valuation fields. J Math Sci 188, 570–581 (2013). https://doi.org/10.1007/s10958-013-1148-5
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DOI: https://doi.org/10.1007/s10958-013-1148-5