Homogeneous skew fields of noncommutative rational functions and their reduced whitehead groups

A construction of skew fields of noncommutative rational fuctions is studied. We discuss and prove criteria 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 com...

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Bibliographic Details
Published inJournal of mathematical sciences (New York, N.Y.) Vol. 183; no. 5; pp. 727 - 747
Main Author Yanchevskii, V. I.
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.06.2012
Subjects
Mathematics
Mathematics and Statistics
Rational Function
Whitehead Group
Reduce Whitehead Group
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Summary:A construction of skew fields of noncommutative rational fuctions is studied. We discuss and prove criteria 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 the reduced Whitehead groups of the corresponding skew fields of noncommutative rational functions. In particular, we present a proof of a previous result by V. P. Platonov and the author concerning the reduced Whitehead groups of skew fields of noncommutative rational functions announced in 1979 and obtain, in the non-Henselian case of such skew fields, analogs of all results of Yu. L. Ershow for the Henselian situation. Bibliography: 31 titles.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-012-0836-x