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Injective stability for K2

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Algebraic K-Theory

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References

  1. J. F. Adams, On the non-existence of elements of Hopf invariant one, Ann. of Math. 72 (1960), 20–103.

    Article  MathSciNet  MATH  Google Scholar 

  2. M. Artin, Théorème de Weil sur la construction d'un groupe à partir d'une loie rationelle, Schémas en Groupes II, SGA 3, Lecture Notes in Math., vol. 152, Springer, Berlin, 1970, 632–653.

    Google Scholar 

  3. M. G. Barratt and M. E. Mahowald, The metastable homotopy of O(n), Bull. Amer. Math. Soc. 70(1964), 758–760.

    Article  MathSciNet  MATH  Google Scholar 

  4. H. Bass, Algebraic K-Theory, Benjamin, New York, 1968.

    MATH  Google Scholar 

  5. R. K. Dennis, Stability for K2, Procedings of the Conference on Orders and Group Rings held at Ohio State University, Columbus, Ohio, May 12–15, 1972, Lecture Notes in Math. 353, Springer, Berlin, 1973, 85–94.

    Google Scholar 

  6. R. K. Dennis and M. R. Stein, Injective Stability for K2 of Local Rings, Bull. Amer. Math. Soc. 80, 1974, 1010–1013.

    Article  MathSciNet  MATH  Google Scholar 

  7. -, The functor K2: A survey of computations and problems, Algebraic K-Theory II, Lecture Notes in Math. 342, Springer, Berlin, 1973, 243–280.

    Google Scholar 

  8. -, K2 of discrete valuation rings, Advances in Math. 18, 1975, 182–238.

    Article  MathSciNet  MATH  Google Scholar 

  9. D. Eisenbud and E. G. Evans, Jr., Generating Modules Efficiently: Theorems from Algebraic K-Theory, J. Algebra 27, 1973, 278–305.

    Article  MathSciNet  MATH  Google Scholar 

  10. S. M. Gersten, Problems about higher K-functors, Algebraic K-Theory I, Lecture Notes in Math. 341, Springer, Berlin, 1973., 43–56 or 41–54.

    MATH  Google Scholar 

  11. S. Hu, Homotopy Theory, Academic Press, New York and London, 1959.

    MATH  Google Scholar 

  12. N. Jacobson, Structure of Rings, Amer. Math. Soc. Colloquium Publications, XXXVII, Providence, Rhode Island, 1964.

    Google Scholar 

  13. N. Jacobson, Lectures in Abstract algebra, II, Van Nostrand, Princeton, 1953.

    Book  MATH  Google Scholar 

  14. W. van der Kallen, The Schur multipliers of SL(3,Z) and SL(4,Z), Math. Ann. 212, 1974, 47–49.

    Article  MathSciNet  MATH  Google Scholar 

  15. W. van der Kallen, The K2 of rings with many units. (in preparation).

    Google Scholar 

  16. W. van der Kallen H. Maazen and J. Stienstra, A presentation for some K2(n,R), Bull. Amer. Math. Soc. 81, 1975, 934–936.

    Article  MathSciNet  MATH  Google Scholar 

  17. M. A. Kervaire, Some non-stable homotopy groups of Lie Groups, Illinois J. Math. 4, 1960, 161–169.

    MathSciNet  MATH  Google Scholar 

  18. M. Mahowald, The metastable homotopy of Sn, Memoirs of the Amer. Math. Soc. 72, Providence, Rhode Island, 1967.

    Google Scholar 

  19. H. Matsumoto, Sur les sous-groupes arithmétiques des groupes semi-simples deployés, Ann. Scient. Ec. Norm. Sup(4) 2, 1969, 1–62.

    MATH  Google Scholar 

  20. J. Milnor, Introduction to Algebraic K-Theory, Annals of Math. Studies 72, Princeton University Press, Princeton, 1971.

    MATH  Google Scholar 

  21. M. R. Stein, Surjective stability in dimension O for K2 and related functors, Trans. Amer. Math. Soc. 178, 1973, 165–191.

    MathSciNet  Google Scholar 

  22. M. R. Stein, Stability theorems for K1,K2 and related functors modelled on Chevalley groups (to appear).

    Google Scholar 

  23. J. R. Strooker, The fundamental group of the general linear group over a ring (preprint).

    Google Scholar 

  24. R. G. Swan, The number of generators of a module, Math. Zeitschrift 102, 1967, 318–322.

    Article  MathSciNet  MATH  Google Scholar 

  25. -Serre's Problem, Conference on Commutative Algebra 1975, Queen's Papers in Pure and Applied Math. 42, Queen's University, Kingston, Ontario, 1975, 1–60.

    Google Scholar 

  26. H. Toda, Composition methods in homotopy groups of spheres, Annals of Math. Studies 49, Princeton University Press, Princeton, 1962.

    MATH  Google Scholar 

  27. L. N. Vaserstein, Stable rank of rings and dimensionality of topological spaces, Funkcional. Anal. i Prilozen (2) 5, 1971, 17–27. (Consultants Bureau Translation, 102–110).

    MathSciNet  MATH  Google Scholar 

  28. -, On the stabilization of Milnor's K2-functor (Russian), Uspehi Mat. Nauk 30, 1, 1975, 224.

    MathSciNet  Google Scholar 

  29. -, On the stabilization of the general linear group over a ring, Math. USSR Sbornik 8, 1969, 383–400.

    Article  MathSciNet  MATH  Google Scholar 

  30. G. D. Whitehead, Homotopy properties of the real orthogonal groups, Ann. of Math. 43, 1942, 132–146.

    Article  MathSciNet  MATH  Google Scholar 

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Michael R. Stein

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© 1976 Springer-Verlag

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van der Kallen, W. (1976). Injective stability for K2 . In: Stein, M.R. (eds) Algebraic K-Theory. Lecture Notes in Mathematics, vol 551. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0079997

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  • DOI: https://doi.org/10.1007/BFb0079997

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  • Print ISBN: 978-3-540-07996-5

  • Online ISBN: 978-3-540-37964-5

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