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Mat. Sb. (N.S.), 1977, Volume 102(144), Number 4, Pages 537–550 (Mi msb2697)  

This article is cited in 37 scientific papers (total in 37 papers)

On stably free modules

A. A. Suslin


Abstract: In this paper we show that if $A$ is an affine algebra of dimension $n$ over an algebraically closed field, then each stably free module whose rank is greater than or equal to $n$ is free. We also obtain some results on orbits of unimodular rows.
Bibliography: 17 titles.

Full text: PDF file (1342 kB)
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English version:
Mathematics of the USSR-Sbornik, 1977, 31:4, 479–491

Bibliographic databases:

UDC: 513.015.7
MSC: Primary 13C10, 15A09; Secondary 16A54, 18F25
Received: 30.07.1976

Citation: A. A. Suslin, “On stably free modules”, Mat. Sb. (N.S.), 102(144):4 (1977), 537–550; Math. USSR-Sb., 31:4 (1977), 479–491

Citation in format AMSBIB
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\by A.~A.~Suslin
\paper On stably free modules
\jour Mat. Sb. (N.S.)
\yr 1977
\vol 102(144)
\issue 4
\pages 537--550
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=441949}
\zmath{https://zbmath.org/?q=an:0354.13005|0389.13002}
\transl
\jour Math. USSR-Sb.
\yr 1977
\vol 31
\issue 4
\pages 479--491
\crossref{https://doi.org/10.1070/SM1977v031n04ABEH003717}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Boratynski M., “Generating Ideals Up to Radical”, Arch. Math., 33:5 (1980), 423–425  mathscinet  zmath  isi
    2. Boratynski M., “Conjecture of Murthy,Mp”, Nagoya Math. J., 77:FEB (1980), 41–45  crossref  mathscinet  zmath  isi
    3. Suslin A., “Mennicke Symbols and their Applications in the K-Theory of Fields”, 966, 1982, 334–356  mathscinet  zmath  isi
    4. Banica C., Forster O., “Complete-Intersections in Stein Manifolds”, Manuscr. Math., 37:3 (1982), 343–356  crossref  mathscinet  zmath  isi
    5. Wilberd van der Kallen, “A group structure on certain orbit sets of unimodular rows”, Journal of Algebra, 82:2 (1983), 363  crossref  mathscinet  zmath
    6. Charles A. Weibel, “Complete intersection points on affine varieties”, Communications in Algebra, 12:24 (1984), 3011  crossref  mathscinet  zmath
    7. S.M Bhatwadekar, “Projective generation of maximal ideals in polynomial rings”, Journal of Algebra, 91:1 (1984), 75  crossref  mathscinet  zmath
    8. Forster O., “Complete-Intersections in Affine Algebraic-Varieties and Stein-Spaces”, Lect. Notes Math., 1092 (1984), 1–28  crossref  mathscinet  zmath  isi
    9. Valla G., “On Set-Theoretic Complete-Intersections”, Lect. Notes Math., 1092 (1984), 85–101  crossref  mathscinet  zmath  isi
    10. Schneider M., “On the Number of Equations Needed to Describe a Variety”, 41, 1984, 163–180  mathscinet  zmath  isi
    11. Roitman M., “On Unimodular Rows”, Proc. Amer. Math. Soc., 95:2 (1985), 184–188  crossref  mathscinet  zmath  isi
    12. Vaserstein L., “Operations on Orbits of Unimodular Vectors”, J. Algebra, 100:2 (1986), 456–461  crossref  mathscinet  zmath  isi
    13. Ravi A. Rao, “Two examples of the Bass-Quillen-Suslin Conjectures”, Math Ann, 279:2 (1987), 227  crossref  mathscinet  zmath  isi
    14. S. Mandal, A. Roy, “Generating ideals in polynomial rings”, Math Z, 195:3 (1987), 315  crossref  mathscinet  zmath  isi
    15. Swan R., “Vector-Bundles, Projective-Modules and the K-Theory of Spheres”, Ann. Math. Stud., 1987, no. 113, 432–522  mathscinet  zmath  isi
    16. Vaserstein L., “Computation of K1 via Mennicke Symbols”, Commun. Algebr., 15:3 (1987), 611–656  crossref  mathscinet  zmath  isi
    17. Nashier B., “On Projective-Modules”, Mon.heft. Math., 104:2 (1987), 119–124  crossref  mathscinet  zmath  isi
    18. Wilberd Van Der Kallen, “A module structure on certain orbit sets of unimodular rows”, Journal of Pure and Applied Algebra, 57:3 (1989), 281  crossref  mathscinet  zmath
    19. Edward K Hinson, “Paths of unimodular vectors”, Journal of Algebra, 142:1 (1991), 58  crossref  mathscinet  zmath
    20. Kumar N., “A Note on Unimodular Rows”, J. Algebra, 191:1 (1997), 228–234  crossref  mathscinet  zmath  isi
    21. Ravi A Rao, “An Abelian Group Structure on Orbits of “Unimodular Squares” in Dimension 3”, Journal of Algebra, 210:1 (1998), 216  crossref  mathscinet  zmath
    22. A. N. Parshin, “Vector Bundles and Arithmetic Groups. II”, Proc. Steklov Inst. Math., 241 (2003), 164–176  mathnet  mathscinet  zmath
    23. S.M. Bhatwadekar, “A cancellation theorem for projective modules over affine algebras over C1-fields”, Journal of Pure and Applied Algebra, 183:1-3 (2003), 17  crossref  mathscinet  zmath
    24. Manoj Kumar Keshari, “Stability results for projective modules over blowup rings”, Journal of Algebra, 294:1 (2005), 226  crossref  mathscinet  zmath
    25. Basu R. Rao R. Khanna R., “On Quillen's Local Global Principle”, Commutative Algebra and Algebraic Geometry, Contemporary Mathematics Series, 390, ed. Ghorpade S. Srinivasan H. Verma J., Amer Mathematical Soc, 2005, 17–30  crossref  mathscinet  zmath  isi
    26. Zeng Z.M., “Set Theoretic Complete Intersection for Curves in a Smooth Affine Algebra”, J. Pure Appl. Algebr., 207:1 (2006), 139–147  crossref  mathscinet  zmath  isi
    27. Zeng Z., “On the Equations Defining Points”, J. Algebra, 299:2 (2006), 679–688  crossref  mathscinet  zmath  isi
    28. Ravi A. Rao, Selby Jose, “Quillen–Suslin theory revisited”, Journal of Pure and Applied Algebra, 211:2 (2007), 541  crossref  mathscinet  zmath
    29. Rao R.A., “A Stably Elementary Homotopy”, Proc. Amer. Math. Soc., 137:11 (2009), 3637–3645  crossref  mathscinet  zmath  isi
    30. Selby Jose, Ravi A. Rao, “A Fundamental Property of Suslin Matrices”, J K-Theory, 2010, 1  crossref  mathscinet  zmath
    31. Rao R.A., Basu R., Jose S., “Injective Stability for K-1 of the Orthogonal Group”, J. Algebra, 323:2 (2010), 393–396  crossref  mathscinet  zmath  isi
    32. N. A. Vavilov, A. V. Stepanov, “Linear groups over general rings. I. Generalities”, J. Math. Sci. (N. Y.), 188:5 (2013), 490–550  mathnet  crossref  mathscinet
    33. Basu R., Chattopadhyay P., Rao R.A., “Some Remarks on Symplectic Injective Stability”, Proc. Amer. Math. Soc., 139:7 (2011), 2317–2325  crossref  mathscinet  zmath  isi
    34. Chattopadhyay P., Rao R.A., “Elementary Symplectic Orbits and Improved K-1-Stability”, J. K-Theory, 7:2 (2011), 389–403  crossref  mathscinet  zmath  isi  elib
    35. J. Fasel, R. A. Rao, R. G. Swan, “On Stably Free Modules over Affine Algebras”, Publ.math.IHES, 116:1 (2012), 223  crossref  mathscinet  zmath
    36. Kodiyalam V., “On the Genesis of a Determinantal Identity”, J. Ramanujan Math. Soc., 28:2 (2013), 173–178  mathscinet  zmath  isi
    37. Selby Jose, R.A.. Rao, “Suslin forms and the Hodge star operator”, Linear Algebra and its Applications, 452 (2014), 328  crossref  mathscinet  zmath
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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