Geodesic
Canonical basis of Hensel--Shafarevich in complete discrete valuation fields
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 22, Tome 394 (2011), pp. 174-193

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Starting with Hensel's generating set of principal units, we construct a base of the module of principal units, in the multiplicative group of a complete descrete valuation field with the residue field of prime characteristic we prove the uniqueness of the above base, and as a corollary, the uniqueness of the canonical Shafarevich base. 
@article{ZNSL_2011_394_a4,
     author = {S. V. Vostokov},
     title = {Canonical basis of {Hensel--Shafarevich} in complete discrete valuation fields},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {174--193},
     publisher = {mathdoc},
     volume = {394},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2011_394_a4/}
}
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S. V. Vostokov. Canonical basis of Hensel--Shafarevich in complete discrete valuation fields. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 22, Tome 394 (2011), pp. 174-193. http://geodesic.mathdoc.fr/item/ZNSL_2011_394_a4/