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Zbl 0705.19001
Levine, Marc
The indecomposable $K\sb 3$ of fields. (English)
[J] Ann. Sci. Éc. Norm. Supér. (4) 22, No. 2, 255-344 (1989). ISSN 0012-9593

The author extends Hilbert's Theorem 90 for $K\sb 2$ of fields - due to Merkur'ev-Suslin - to the relative $K\sb 2$ of semi-local principal ideal rings containing a field. This yields a computation of the torsion and cotorsion of the indecomposable $K\sb 3$ of a field. The main results of the paper have independently been obtained by {\it A. S. Merkur'ev} and {\it A. A. Suslin} [Izv. Akad. Nauk SSSR, Ser. Mat. 54, No.3, 522-545 (1990)] with a slightly different method.
[M.Kolster]

MSC 2000:: *19D50 Computations of higher K-theory of rings
13D15 K-theory (commutative rings)
19F99 K-theory in number theory

Keywords: Hilbert 90; relative $K\sb 2$ of semi-local principal ideal rings containing a field; computation of the torsion and cotorsion of the indecomposable $K\sb 3$ of a field

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