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 Zap. Nauchn. Sem. POMI, 2011, Volume 388, Pages 270–308 (Mi znsl4114)

Homogeneous skew-fields of non-commutative rational functions and their reduced Whitehead groups

V. I. Yanchevskiĭ

Institute of Mathematics of the National Academy of Sciences of Belarus

Abstract: 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.

Key words and phrases: reduced Whitehead group, skew-field of non-commutative rational functions, special linear group of finite-dimensional central simple algebra, skew polynomial ring.

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English version:
Journal of Mathematical Sciences (New York), 2012, 183:5, 727–747

UDC: 514.142

Citation: V. I. Yanchevskiǐ, “Homogeneous skew-fields of non-commutative rational functions and their reduced Whitehead groups”, Problems in the theory of representations of algebras and groups. Part 21, Zap. Nauchn. Sem. POMI, 388, POMI, St. Petersburg, 2011, 270–308; J. Math. Sci. (N. Y.), 183:5 (2012), 727–747

Citation in format AMSBIB
\Bibitem{Yan11} \by V.~I.~Yanchevski{\v\i} \paper Homogeneous skew-fields of non-commutative rational functions and their reduced Whitehead groups \inbook Problems in the theory of representations of algebras and groups. Part~21 \serial Zap. Nauchn. Sem. POMI \yr 2011 \vol 388 \pages 270--308 \publ POMI \publaddr St.~Petersburg \mathnet{http://mi.mathnet.ru/znsl4114} \transl \jour J. Math. Sci. (N. Y.) \yr 2012 \vol 183 \issue 5 \pages 727--747 \crossref{https://doi.org/10.1007/s10958-012-0836-x} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84862295875}