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Izv. Akad. Nauk SSSR Ser. Mat., 1988, Volume 52, Issue 2, Pages 310–335 (Mi izv1182)  

This article is cited in 1 scientific paper (total in 1 paper)

The group $SK_2$ for quaternion algebras

A. S. Merkur'ev


Abstract: The injectivity of the reduced norm homomorphism $K_2(D)\to K_2(F)$ for the quaternion algebra $D=\binom{a,b}F$, defined over a field $F$ of characteristic $\ne2$, is proved. It is proved that the group $K_2(D)$ can be identified with the subgroup of $K_2(F)$ consisting of all $u$ such that the product $u\cdot\{a,b\}$ is divisible by $2$ in the Milnor group $K_4^M(F)$.
Bibliography: 21 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1989, 32:2, 313–337

Bibliographic databases:

UDC: 519.46
MSC: Primary 16A39, 18F25; Secondary 19C20
Received: 02.07.1986

Citation: A. S. Merkur'ev, “The group $SK_2$ for quaternion algebras”, Izv. Akad. Nauk SSSR Ser. Mat., 52:2 (1988), 310–335; Math. USSR-Izv., 32:2 (1989), 313–337

Citation in format AMSBIB
\Bibitem{Mer88}
\by A.~S.~Merkur'ev
\paper The group $SK_2$ for quaternion algebras
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1988
\vol 52
\issue 2
\pages 310--335
\mathnet{http://mi.mathnet.ru/izv1182}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=941679}
\zmath{https://zbmath.org/?q=an:0665.12012|0652.12006}
\transl
\jour Math. USSR-Izv.
\yr 1989
\vol 32
\issue 2
\pages 313--337
\crossref{https://doi.org/10.1070/IM1989v032n02ABEH000764}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. S. Merkur'ev, A. A. Suslin, “The norm residue homomorphism of degree three”, Math. USSR-Izv., 36:2 (1991), 349–367  mathnet  crossref  mathscinet  zmath  adsnasa
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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