Stabilization theorem for the Milnor K2-functor

A. A. Suslin; M. S. TuLenbaev

doi:10.1007/BF01091768

Stabilization theorem for the Milnor K₂-functor

A. A. Suslin, M. S. TuLenbaev

Mathematics

Research output: Contribution to journal › Article › peer-review

21 Scopus citations

Abstract

Let Λ be an associative ring. For every natural number n there is a canonical homomorphism ψ_n: K_2,n(Λ)→K₂(Λ), where K₂ is the Milnor functor and K_2,n(Λ) the associated unstable K-group. Dennis and Vasershtein have proved that if n is larger than the stable rank of Λ, ψ_n is an epimorphism. It is proved in the article that if n - 1 is greater than the stable rank of Λ, the homomorphism ψ_n is an isomorphism.

Original language	English (US)
Pages (from-to)	1804-1819
Number of pages	16
Journal	Journal of Soviet Mathematics
Volume	17
Issue number	2
DOIs	https://doi.org/10.1007/BF01091768
State	Published - Sep 1981

ASJC Scopus subject areas

Statistics and Probability
General Mathematics
Applied Mathematics

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N2 - Let Λ be an associative ring. For every natural number n there is a canonical homomorphism ψn: K2,n(Λ)→K2(Λ), where K2 is the Milnor functor and K2,n(Λ) the associated unstable K-group. Dennis and Vasershtein have proved that if n is larger than the stable rank of Λ, ψn is an epimorphism. It is proved in the article that if n - 1 is greater than the stable rank of Λ, the homomorphism ψn is an isomorphism.

AB - Let Λ be an associative ring. For every natural number n there is a canonical homomorphism ψn: K2,n(Λ)→K2(Λ), where K2 is the Milnor functor and K2,n(Λ) the associated unstable K-group. Dennis and Vasershtein have proved that if n is larger than the stable rank of Λ, ψn is an epimorphism. It is proved in the article that if n - 1 is greater than the stable rank of Λ, the homomorphism ψn is an isomorphism.

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Stabilization theorem for the Milnor K₂-functor

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