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JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

Zap. Nauchn. Sem. LOMI, 1976 Volume 64, Pages 131–152 (Mi znsl1879)

This article is cited in 23 papers

Stabilization theorem for the Milnor $K_2$-functor

A. A. Suslin, M. S. Tulenbaev


Abstract: Let $\Lambda$ be an associative ring. For every natural number $n$ there is a canonical homomorphism $\Psi_n\colon K_{2,n}(\Lambda)\to K_2(\lambda)$ where $K_2$ is the Milnor functor and $K_{2,n}(\lambda)$ the associated unstable $K$-group. Dennis and Vasershtein have proved that if $n$ is larger than the stable rank of $\Lambda$, $\Psi_n$is an epimorphism. It is proved in the article that if $n-1$ is greater than the stable rank of $\Lambda$, the homomorphism $\Psi_n$ is an isomorphism.

UDC: 519.46


 English version:
Journal of Soviet Mathematics, 1981, 17:2, 1804–1819

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