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Stabilization theorem for the Milnor K2-functor

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Abstract

Let Λ be an associative ring. For every natural number n there is a canonical homomorphismψ n: 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,ψ n is an epimorphism. It is proved in the article that if n − 1 is greater than the stable rank of Λ, the homomorphismψ n is an isomorphism.

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Literature cited

  1. H. Bass, Algebraic K-Theory, Springer-Verlag (1973).

  2. H. Bass, “Liberation des modules projectifs sur certains anneaux de polynomes,” in: Lect. Notes Math., Vol. 431, Springer-Verlag, New York (1975), pp. 228–254.

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  3. L. N. Vasershtein, “K1-theory and the congruence subgroup problem,” Mat. Zametki,5, No. 2, 233–244 (1969).

    Google Scholar 

  4. L. N. Vasershtein, “Stable rank of rings and dimension of topological spaces,” Funkts. Anal. Prilozhen.,5, No. 2, 17–27 (1971).

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  5. L. N. Vasershtein and A. A. Suslin, “Serre's problem on projective modules over polynomial rings and algebraic K-theory,” Funkts. Anal. Prilozhen.,8, No. 2, 65–67 (1974).

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  6. R. K. Dennis, “Surjective stability for the functor K2,” in: Lect. Notes Math., Vol. 353, Springer-Verlag, New York (1973), pp. 85–94.

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  7. R. K. Dennis and M. R. Stein, “The functor K2: a survey of computations and problems,” in: Lect. Notes Math., Vol. 342, Springer-Verlag, New York (1973), pp. 243–280.

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  8. J. Milnor, Introduction to Algebraic K-Theory, Princeton Univ. Press (1972).

  9. A. A. Suslin, “On stable rank of polynomial rings and algebras over fields,” in: Proc. All-Union Algebraic Symp. [in Russian], Part 2, Gomel' (1975).

  10. L. N. Vasershtein, “Stabilization for the Milnor K2-functor,” Usp. Mat. Nauk,30, No. 1, 224 (1975).

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Authors
  1. A. A. Suslin
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  2. M. S. TuLenbaev
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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 64, pp. 131–152, 1976.

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Suslin, A.A., TuLenbaev, M.S. Stabilization theorem for the Milnor K2-functor. J Math Sci 17, 1804–1819 (1981). https://doi.org/10.1007/BF01091768

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  • DOI: https://doi.org/10.1007/BF01091768

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