Geodesic
Multiplicative representation of principal units in two-dimentional complete fields
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 6, Tome 265 (1999), pp. 11-21 Cet article a éte moissonné depuis la source Math-Net.Ru

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This paper gives conditions on existence and uniqueness of representation of principal units in two-dimentional complete fields as a product of principal units from some fixed set. 
@article{ZNSL_1999_265_a1,
     author = {V. G. Boitsov},
     title = {Multiplicative representation of principal units in two-dimentional complete fields},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {11--21},
     year = {1999},
     volume = {265},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1999_265_a1/}
}
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V. G. Boitsov. Multiplicative representation of principal units in two-dimentional complete fields. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 6, Tome 265 (1999), pp. 11-21. http://geodesic.mathdoc.fr/item/ZNSL_1999_265_a1/