Academic Research

DAVID M. ARNOLD – Research

RESEARCH INTERESTS

Torsion-free abelian groups of finite rank and related topics, such as representations of finite partially ordered sets, torsion-free modules of finite rank over a discrete valuation ring, subrings of algebraic number fields, finitely generated modules over multiple pullback rings, and lattices over orders

BOOKS PUBLISHED

1. Finite Rank Torsion-free Abelian Groups and Rings, Lecture Notes in Mathematics 931, Springer-Verlag, New York, 1982, 191 pp.
2. Abelian Groups and Representations of Partially Ordered Sets, CMS Advanced Books in Mathematics, Springer-Verlag, New York, 2000, 244 pp.

CONFERENCE PROCEEDINGS (CO-EDITOR)

1. Abelian Group Theory, Lecture Notes in Mathematics, 616, Springer-Verlag, New York, 1977, 423 pp
2. Abelian Groups and Modules, Pure and Applied Math., Marcel Dekker, New York, 1996, 411 pp
3. Abelian Groups and Modules, Proceedings of 2001 Honolulu Conference on Abelian Groups and Modules, entire issue of Rocky Mountain Journal of Mathematics, Vol. 3, Winter 2002, 610 pp

RESEARCH PUBLICATIONS IN REFEREED JOURNALS

  1. A duality for torsion free modules of finite rank over discrete valuation rings, Proc. London Math. Soc. 24 (3) (1972), 204-216.
  2. A duality for torsion free abelian groups, Pac. J. Math. 42 (1972), 11-15.
  3. Exterior powers and torsion free modules, Trans. A.M.S. 170 (1972), 471-481.
  4. Algebraic K-theory of torsion free abelian groups, Symposia Mathematica Vol. XIII, Academic Press, 1974, 179-193.
  5. Grothendieck and Whitehead groups of torsion-free abelian groups, Bull. A.M.S., 19 (1973), 723-724.
  6. A class of pure subgroups of completely decomposable abelian groups, Proc. A.M.S. 41 (1973), 37-44.
  7. Endomorphism rings and direct sums of torsion free abelian groups, Trans. A.M.S. 211 (1975), 225-237 (with E.L. Lady).
  8. Abelian groups A such that Hom(A,-) preserves direct sums of copies of A, Pacific J. Math., 56 (1975), 7-20 (with C. E. Murley).
  9. Quasi-pure projective and injective torsion free abelian groups of rank two, Rocky Mountain J. Math. 6 (1976), 61-70 (with C. Vinsonhaler and W. Wickless).
  10. Strongly homogeneous torsion free abelian groups of finite rank, Proc. A.M.S. 56 (1976), 67-72.
  11. Genera and direct sum decompositions of torsion free modules, Springer-Verlag Lecture Notes in Mathematics 616, 1977, 197-218.
  12. Quasi-pure projective and injective torsion free Abelian groups of finite rank, Proc. London Math. Soc. 38 (3), 1979, 532-544 (with B. O’Brien and J. Reid).
  13. Summands of direct sums of cyclic valuated groups, Symposia Mathematica Vol XXIII, Academic Press, 1979, 79-84 (with R. Hunter and E. Walker).
  14. Global Azumaya Theorems in additive categories, J. Pure and Appl. Alg 16 (1980) 223-242 (with R. Hunter and F. Richman).
  15. Torsion- free abelian groups of finite rank projective as modules over their endomorphism rings, J. of Alg., 71 (1981), 1-10 (with R. Pierce, J. Reid, C. Vinsonhaler, and W. Wickless).
  16. Pure subgroups of finite rank completely decomposable groups, Abelian Group Theory, Springer-Verlag Lecture Notes in Mathematics 874, 1981, 1-31.
  17. Endomorphism rings and subgroups of finite rank torsion-free abelian groups, Rocky Mountain J. Math., 12 (1982), 241-256.
  18. Pure subgroups of finite rank completely decomposable groups II, Abelian Group Theory, Springer-Verlag Lecture Notes in Mathematics 1006, 1983, 97-143 (with C. Vinsonhaler).
  19. A finite global Azumaya theorem in additive categories, Proc. A.M.S. 91 (1984), 25-30.
  20. Typesets and cotypesets of rank-2 torsion-free Abelian groups, Pac. J. Math. 114 (1984), 1-21 (with C. Vinsonhaler).
  21. Notes on Butler groups and balanced extensions, Boll. Unione Mat. Ita., (6) 5-A (1986), 175-184.
  22. Representing graphs for a class of torsion-free abelian groups, Abelian Group Theory Gordon & Breach, 1987, 309-332 (with C. Vinsonhaler).
  23. Endomorphism rings of Butler groups, Jour. Aust. Math. Soc., 42 (1987), 322-329 (with C. Vinsonhaler).
  24. Subgroups of finite direct sums of valuated cyclic groups, J. Alg. 114 (1988), 1-15 (with F. Richman).
  25. Quasi-isomorphism invariants for a class of torsion-free abelian groups, Houston J. Math. 159 (1989), 327-340 (with C. Vinsonhaler).
  26. A characterization of modules with the summand intersection property, Comm. in Alg. 18 (1990), no. 2, 519-526 (with J. Hausen).
  27. Representations of partially ordered sets and abelian groups, Abelian Group Theory, Contemporary Mathematics 87, A.M.S., 1989, 91-110.
  28. Quasi-endomorphism rings for a class of Butler groups, Abelian Group Theory, Contemporary Mathematics 87, A.M.S., 1989, 85-90 (with C. Vinsonhaler).
  29. Invariants for a class of torsion-free abelian groups, Proc. A.M.S. 105 (1989), 293-300 (with C. Vinsonhaler).
  30. Duality and invariants for Butler groups, Pac. J. Math. 148 (1991) (with C. Vinsonhaler).
  31. Isomorphism invariants for Abelian groups, Trans. A.M.S. 330 (1992), 711-724 (with C. Vinsonhaler).
  32. Invariants for classes of representations of finite posets, J. Alg. 147 (1992), 245-264 (with C. Vinsonhaler).
  33. Almost split sequences for Dedekind-like rings, J. London Math Soc., (2) 43 (1991), 225-235 (with R. Laubenbacher).
  34. Field-independent representations of posets, Forum Math., 4 (1992), 349-357 (with F. Richman).
  35. General p-valuations, Comm. In Alg. 19 (1991), 3075-3088 (with F. Richman and C. Vinsonhaler)
  36. Representations of lattices in additive categories, Comm. in Alg. 22 (9) (1994), 3277-3295 (with C. Vinsonhaler).
  37. Almost split sequences for Dedekind-like rings II, Comm. in Alg. 23 (1995), 11-130 (with R. Laubenbacher).
  38. Butler groups with finite typesets and free groups with distinguished subgroups, Comm. in Alg., 21 (1993), 1947-1982 (with M. Dugas).
  39. Block rigid almost completely decomposable groups and lattices over multiple pullback rings, J. Pure and Appl. Alg., 87 (1993), 105-121 (with M. Dugas).
  40. Locally free finite rank Butler groups and near isomorphism, Abelian Groups and Modules, Kluwer, Boston, 1995, 41-48 (with M. Dugas).
  41. Representations of finite posets and near isomorphism of finite rank Butler groups, Rocky Mtn. J. Math 25 (1995), 591-609 (with M. Dugas).
  42. Butler groups, representations of finite posets, and modules over multiple pullback rings, Methods in Module Theory, Lecture Notes in Pure and Applied Mathematics 140, Marcel Dekker, New York, 1993, 1-18.
  43. Quasi-isomorphism invariants for two classes of finite rank Butler groups, Proc. A.M.S., 118 (1993), 19-26 (with C. Vinsonhaler).
  44. Finite rank Butler groups, a survey of recent results, Abelian Groups, Marcel Dekker, New York, 1993, 17-41 (with C. Vinsonhaler).
  45. Almost split sequences, representations of finite posets, and finite rank Butler groups, Abelian Groups, Marcel Dekker, New York, 1993, 79-95 (with C. Vinsonhaler).
  46. Indecomposable modules over Nagata valuation domains, Proc. A.M.S. 122 (1994), 689-696(with M. Dugas)
  47. Finitely generated modules over pullback rings, J. Alg., 184 (1996), 302-332 (with R. Laubenbacher).
  48. Near isomorphism of Butler groups and representations of finite posets, Abelian Groups and Modules, Kluwer, Boston, 1995, 29-40.
  49. A survey of Butler groups and the role of representations, Abelian Groups and Modules, Pure and Applied Math. 182, Marcel Dekker, New York, 1996, 1-14.
  50. Finitely generated modules over pullback rings and algebras, Advances in Algebra and Model Theory, Gordon and Breach, 1997, 401-414.
  51. Representation type of posets and finite rank Butler groups, Colloquium Mathematicum, 74 (1997), 299-320 (with M. Dugas).
  52. Representation type of posets and almost completely decomposable groups, Forum Math. 10 (1998), 729-749 (with M. Dugas).
  53. Finite rank Butler groups and torsion-free modules over a discrete valuation ring, Proc. A.M.S. 129 (2001), 325-335 (with M. Dugas and K.M. Rangaswamy)
  54. Finite rank Butler groups with small typesets, Abelian Groups and Modules, Birkhauser-Verlag, Boston, 1999, 107-120 (with M. Dugas)
  55. Co-purely indecomposable module, J. Pure and Applied Algebra, 161 (2001), 1-12 (with M. Dugas).
  56. Direct sum decompositions of torsion-free abelian groups, Abelian Groups, Rings, and Modules, Contemporary Math. A.M.S., Providence, Rhode Island, 2001, 65-74.
  57. Torsion-free modules of finite rank over a discrete valuation ring, J. Algebra 272 (2004), 456-69 (with M. Dugas and K.M. Rangaswamy).
  58. Direct Sums of Local Torsion-Free Abelian Groups, Proc. A.M.S. 130 (2002), 1611-1617.
  59. Endo-wild representation type and generic representations of finite posets Pacific J. Math., 219 (2005), 101-126 (with D. Simson).
  60. Mixed modules over a discrete valuation ring, Forum Math., 18 (2006), 85-98 (with K.M. Rangaswamy).
  61. Representations of finite partially ordered sets over commutative artinian uniserial rings, J. Pure and Appl. Alg, 205 (2006), 640-659 (with Daniel Simson).
  62. Representations of finite partially ordered sets over discrete valuation rings, Comm. In Alg. 35 (2007), 3128-3144 (with Daniel Simson)
  63. Pi-balanced torsion-free modules over a discrete valuation ring, J. Algebra 295 (2006), no. 1, 269-288 (with K.M. Rangaswamy and F. Richman).
  64. Pure submodules of finite direct sums of co-purely indecomposable modules, Comm. in Alg. 35 (2007), 355-369 (with K.M. Rangaswamy).
  65. A note on countable Butler groups and pure subgroups of completely decomposable groups, Bollettino U. M. I., (8) 10-B (2007), 605-611 (with K. M. Rangaswamy).
  66. Subgroups of finite direct sums of Z[1/n], Houston J. Math., 34, No. 4 (2008), 997-1008.
  67. Locally free abelian groups of finite rank, Models, Modules and Abelian Groups, de Gruyter, Berlin-New York, 2008, 83-97.
  68. Indecomposable (1,3)-groups and a matrix problem, Czech. Math. Journal, no. 2 (2013), 307-355 (with A. Mader, O. Mutzbauer, E. Solak)
  69. Almost completely decomposable groups and unbounded representation type, J. Alg. 349 (2012), 50 – 62. (with A. Mader, O. Mutzbauer, E. Solak)
  70. Representations of posets and indecomposable torsion-free abelian groups, Comm. In Alg., accepted for publication, 9/15/12. (with A. Mader, O. Mutzbauer, E. Solak)
  71. Indecomposable (1,3)-groups with homocyclic regulator quotients of exponent p4 have rank 4,5,6, accepted for publication, J. Alg., July, 2013 (with A. Mader, O. Mutzbauer, E. Solak)
  72. Representations of posets and decompositions of torsion-free abelian groups, to be submitted for publication, Turkey Conference (with A. Mader, O. Mutzbauer, E. Solak).

EXPOSITORY REFEREED ARTICLES

  1. An introduction to the structure of abelian groups, Cubo-Matema’tica Educacional, Universidad de la Frontera, Vol. 4, No. 1 (2002), pp 151-168
  2. International conferences on abelian group theory; the first forty years, Rocky Mountain Journal of Mathematics, Vol. 3, Winter, 2002, 1153-1160

REFEREEING ACTIVITIES (2000 – present)

A. Mathematical research journals/books:
1. Communications in Algebra
2. Article for “Models, Modules and Abelian Groups”, de Gruyter
3. Journal of Algebra
4. Journal of Pure and Applied Algebra
5. Book Proposal, Discrete Valuation Rings, Springer-Verlag
6. Publicationes Mathematicae Debrecen
7. Rocky Mountain Journal of Mathematics
8. Illinois Journal of Mathematics
9. Israel Journal of Mathematics
10. Proceedings, American Mathematical Society
11. Bulletin, Iranian Mathematical Society
12. Houston Journal of Mathematics
13. Chapter for “Handbook of Algebra”

B. Math Reviews
Numerous reviews of research articles and books

C. Grant Proposals Refereed
National Science Foundation
National Sciences and Engineering Research Council of Canada
National Security Agency
South African National Research Foundation