Geodesic
Homogeneous skew-fields of non-commutative rational functions and their reduced Whitehead groups
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 21, Tome 388 (2011), pp. 270-308

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A construction of skew-fields of non-commutative rational functions is studied. We discuss and prove criterions for such skew-fields to be homogeneous and finite-dimensional over their centers and describe relations between some objects defined in terms of the skew-fields of constants, which help to compute reduced Whitehead groups of corresponding skew-fields of non-commutative rational functions. In particular we present a proof of one previous result of V. P. Platonov and the author about reduced Whitehead groups of skew-fields of non-commutative rational functions announced in 1979 and obtain in non-Henselian case of such skew-fields analogues of all results of Yu. L. Ershov for Henselian situation. 
@article{ZNSL_2011_388_a11,
     author = {V. I. Yanchevskiǐ},
     title = {Homogeneous skew-fields of non-commutative rational functions and their reduced {Whitehead} groups},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {270--308},
     publisher = {mathdoc},
     volume = {388},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2011_388_a11/}
}
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V. I. Yanchevskiǐ. Homogeneous skew-fields of non-commutative rational functions and their reduced Whitehead groups. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 21, Tome 388 (2011), pp. 270-308. http://geodesic.mathdoc.fr/item/ZNSL_2011_388_a11/