Publications - R.G.Swan

  1. A new method in fixed point theory, Bull. Amer. Math. Soc. 65 (1959), 128-130 (abstract of (7)).
  2. The homology of cyclic products, Bull. Amer. Math. Soc. 65 (1959), 125-127 (abstract of (8)).
  3. Projective modules over finite groups, Bull. Amer. Math. Soc. 65 (1959), 365-367 (abstract of (9)).
  4. Groups with periodic cohomology, Bull. Amer. Math. Soc. 65 (1959), 368-370 (abstract of (10)).
  5. (with S. Sternberg) On maps with non-negative Jacobian, Mich. Math. J. 6 (1959), 339-342.
  6. A simple proof of the cup product reduction theorem, Proc. Nat. Acad. Sci. 46 (1960), 114-117.
  7. A new method in fixed point theory, Comment. Math. Helv. 34 (1960), 1-16.
  8. The homology of cyclic products, Trans. Amer. Math. Soc. 95 (1960), 27-68.
  9. Induced representations and projective modules, Ann. of Math. 71 (1960), 552-578.
  10. Periodic resolutions for finite groups, Ann. of Math. 72 (1960), 267-291.
  11. The p-period of a finite group, Ill. J. Math. 4 (1960), 341-346.
  12. The non-triviality of the restriction map in the cohomology of groups,
    Proc. Amer. Math. Soc. 11 (1960), 885-887.
  13. (with W. H. Cockcroft) On the homotopy type of certain two dimensional complexes,
    Proc. London Math. Soc. (3) 11 (1961), 194-202.
  14. Projective modules over group rings and maximal orders, Ann. of Math. 76 (1962), 55-61.
  15. Factorization of polynomials over finite fields, Pacific J. Math. 12 (1962), 1099-1106.
  16. An application of graph theory to algebra, Proc. Amer. Math. Soc. 14 (1963), 367-373 (see also (28)).
  17. Vector bundles and projective modules, Trans. Amer. Math. Soc. 105 (1962), 264-277.
  18. The Grothendieck ring of a finite group, Topology 2 (1963), 85-110.
  19. The Theory of Sheaves, The University of Chicago Press 1964.
  20. (with H. Bass and A. Heller) The Whitehead group of a polynomial extension,
    Publ. Math. I. H. E. S. 22 (1964), 61-79.
  21. Minimal resolutions for finite groups, Topology 4 (1965), 193-208.
  22. The number of generators of a module, Math. Z. 102 (1967), 318-322.
  23. Representations of polycyclic groups, Proc. Amer. Math. Soc. 18 (1967), 573-574.
  24. Algebraic K-Theory, Lecture Notes in Math. 76, Springer-Verlag, Berlin 1968.
  25. Generators and relations for certain special linear groups, Bull. Amer. Math. Soc. 74 (1968), 576-581
    (abstract of (30)).
  26. Invariant rational functions and a problem of Steenrod, Invent. Math. 7 (1969), 148-158.
  27. Groups of cohomological dimension one, J. Algebra 12 (1969), 585-610.
  28. Correction to "An application of graph theory to algebra", Proc. Amer. Math. Soc. 21 (1969), 379-380 (see (16)).
  29. Non-abelian homological algebra and K-theory, pp. 88-133 in "Applications of Categorical Algebra, New York 1968", Proc. Symp. Pure Math XVII, Amer Math. Soc., Providence 1970.
  30. Generators and relations for certain special linear groups, Adv. in Math. 6 (1981), 1-77.
  31. Groups with no odd dimensional cohomology, J. Algebra 17 (1971), 401-403.
  32. K-Theory of Finite Groups and Orders, Notes by E. G. Evans, Lecture Notes in Math. 149,
    Springer-Verlag, Berlin 1970.
  33. A splitting principle in algebraic K-theory, pp. 155-159 in "Representation theory of finite groups and related topics", Proc. Symp. Pure Math. XXV, Amer. Math. Soc., Providence, 1971.
  34. Algebraic K-theory, Actes Congr. Intern. Math. 1970, Tome 1, 191-199.
  35. Excision in algebraic K-theory, J. Pure Appl. Alg. 1 (1971), 221-252.
  36. Some relations between higher K-functors, J. Algebra 21 (1972), 113-136.
  37. K-theory and algebraic correspondences, pp. 161-179 in Lecture Notes in Math. 353, Springer-Verlag, Berlin 1973.
  38. Problems in algebraic K-theory, Proceedings of the Seattle Conference on Algebraic K-Theory,
    Lecture Notes in Math. 341,342, Springer-Verlag, Berlin 1972.
  39. A cancellation theorem for projective modules in the metastable range, Invent. Math. 27 (1974), 23-43.
  40. (with J. Towber) A class of projective modules which are nearly free, J. Algebra 36 (1975), 427-434.
  41. Thom's theory of differential forms on simplicial sets, Topology 14 (1975), 271-273.
  42. (with M. P. Murthy) Vector bundles over affine surfaces, Invent. Math. 36 (1976), 125-165.
  43. Serre's problem, Conf. on Comm. Algebra, Queen's papers in Pure and Appl. Math. 42,
    Queen's University, Kingston, Ont. 1975.
  44. Topological examples of projective modules, Trans. Amer. Math. Soc. 230 (1977), 201-234.
  45. Projective modules over Laurent polynomial rings, Trans. Amer. Math. Soc. 237 (1978), 111-120.
  46. Strong approximation and locally free modules, pp. 153-223 in "Ring Theory and Algebra III", ed. B. R. McDonald, Marcel Dekker, New York 1980.
  47. On seminormality, J. Algebra 67 (1980), 210-229.
  48. Galois theory, in "Emmy Noether: A tribute to her life and work", ed. J. W. Brewer and M. K. Smith,
    Marcel Dekker, New York 1981.
  49. Noether's problem in Galois theory, in "Emmy Noether in Bryn Mawr" ed. B. Srinivasan and J. Sally,
    Springer-Verlag, New York 1983.
  50. Projective modules over binary polyhedral groups, J. reine angew. Math. 342(1983),66-172.
  51. N-generator ideals in Pruefer domains, Pacific J. Math. 111 (1984), 433-446.
  52. Vector bundles, projective modules, and the K-theory of spheres, Proc. of the John Moore Conference,
    Algebraic Topology and Algebraic K-Theory, ed. W. Browder, Ann. of Math. Study 113 (1987),432-522.
  53. K-Theory of quadric hypersurfaces, Ann. of Math. 122 (1985), 113-153.
  54. (with E. Hamann) Two counterexamples in power series rings, J. Algebra 100 (1986), 260-264.
  55. (with L. N. Vaserstein) On the absolute stable range of rings of continuous functions, Applications of algebraic K-theory to algebraic geometry and number theory, Contemp. Math. 55 (1986), 689-692.
  56. Torsion free cancellation over orders, Illinois J. Math. 32 (1988), 329-360.
  57. A simple proof of Gabber's theorem on projective modules over a localized local ring,
    Proc. Amer. Math. Soc. 103 (1988), 1025-1030.
  58. Zero cycles on quadric hypersurfaces, Proc. Amer. Math. Soc. 107 (1989), 43-46.
  59. Another proof of the quadratic reciprocity theorem?, Amer. Math. Monthly 97 (1990), 138-139.
  60. Gubeladze's proof of Anderson's conjecture, Proceedings of the Azumaya Conference, Indiana University,Contemporary Math. 124 (1992), 215-250.
  61. Failure of cancellation for direct sums of line bundles, Trans. Amer. Math. Soc.,336 (1993), 581-605.
  62. Algebraic vector bundles on the 2-sphere, Rocky Mountain J. Math. 23 (1993), 1443-1469.
  63. Quaternionic bundles on algebraic spheres, Rocky Mountain J. Math. 26 (1996), 773-791.
  64. Higher algebraic K-theory (expository paper), Proceedings of the Santa Barbara Conference on Quadratic Forms, Proc. Symp. Pure Math. 58 vol.1 (1995), 247-293.
  65. (with A. Adem) Linear maps over abelian group algebras, J. Pure App. Alg. 104 (1995), 1-7.
  66. Hochschild cohomology of quasiprojective schemes, J. Pure App. Alg. 110 (1996), 57-80.
  67. Neron-Popescu desingularization (expository paper), in Algebra and Geometry,
    Proc. Internat. Conf. of Algebra and Geometry, ed. M-c. Kang, International Press 1998.
  68. A simple proof of Rankin's campanological theorem, Amer. Math. Monthly, 106 (1999), 159-161.
  69. Cup products in sheaf cohomology, pure injectives, and a substitute for projective resolutions,
    J. Pure App. Alg. 144 (1999), 169-211.
  70. Hilbert's theorem on positive ternary quartics, in Quadratic Forms and their Applications,
    Contemp. Math. 272, Amer. Math. Soc. 2000, 287-292.
  71. Failure of cancellation over group algebras, Appendix (pp. 232--233) to:
    D. Khurana and T. Y. Lam, Rings with internal cancellation, J. Algebra 284(2003), 203-235.
  72. (with S. McAdam) Unique comaximal factorization, J. Algebra 276(2004), 180--192.
  73. (with S. McAdam) Factorizations of monic polynomials, pp. 411-424 in
    Rings, Modules, Algebras, and Abelian Groups, Lecture Notes in Pure and Appl. Math., 236
    ed. A. Facchini,E. Houston, and L. Salce, Marcel Dekker, New York, 2004.
  74. (with S. McAdam) A special type of invertible ideal, pp. 356-362 in
    Arithmetical properties of commutative rings and monoids, Lecture Notes in Pure and Appl. Math., 241
    Chapman & Hall/CRC, Boca Raton, FL, 2005.
  75. (with T. Y. Lam) Sums of alternating matrices and invertible matrices, pp. 201-211 in
    Algebra and its applications, Contemp. Math., 419, Amer. Math. Soc., Providence, RI, 2006.
  76. (with Vijay Kodiyalam and T. Y. Lam) Determinantal ideals, Pfaffian ideals, and the principal minor theorem, pp. 35-60 in
    Noncommutative rings, group rings, diagram algebras and their applications, Contemp Math. 456 Amer. Math. Soc., Providence, RI, 2008.
  77. (with T. Y.Lam) Symplectic modules and von Neumann regular matrices over commutative rings, pp. 213-227 in
    Advances in Ring Theory, ed. D. V. Huynh and S. R. Lopez-Permouth, Birkhauser/Springer Basel AG, 2010.