Andy R. Magid
                           Publications

                              PAPERS

  1. "Commutative algebras of Hochschild dimension one", Proc.  Amer. Math. Soc. 24(1970), 530-532

  2. "Locally Galois algebras", Pacific J. Math 33(1970), 707-724

  3. "Pierce's representation and separable algebras", Ill. J.  Math. 15(1971), 114-121

  4. "Galois groupoids", J. of Algebra 18(1971), 89-102

  5. "Abelian extensions of rings of positive characteristic",  Rocky Mt. Journal 2(1972), 311-315

  6. "Finite group schemes over fields" (with R. Hoobler), Proc. Amer. Math. Soc. 33(1972), 310-312

  7. "The separable closure of some commutative rings", Trans. Amer. Math. Soc. 169(1972), 109-124

  8. "A separably closed ring with non-zero torsion Pic", Pacific J. Math. 42(1972), 711-714

  9. "K-theory of commutative regular rings", Proc. Amer. Math. Soc. 39(1973), 489-492

  10. "A Van Kampen theorem for separable algebras", Proc. Amer. Math. Soc. 39(1973), 483-488

  11. "Invariant subrings of separable algebras", Israel J. Math. 16(1973), 306-313

  12. "The Picard invariant of a principal homogeneous space"  (with L. Childs), J. Pure Applied Algebra 4(1974), 273-286

  13. "Principal homogeneous spaces and Galois algebras", Pacific J. Math. 53(1974), 501-513

  14. "Algebraically separable extensions of Banach algebras", Michigan J. Math. 21(1974), 137-143

  15. "Fundamental groups of products", Comm. in Algebra 3(1974),  37-46

  16. "Trigonometric identities", Math. Mag. 47(1974), 226-227, reprinted in HARMONY OF THE WORLD:75 YRS OF MATH MAG, Gerald L. Alexanderson & Peter Ross, Editors, Mathematical Association of America, Washington, DC, 2007

  17. "Ultrafunctors", Canadian J. Math. 27(1975), 372-375

  18. "K2 of von Neumann regular rings" (with K. Dennis), J. Pure Applied Algebra 6(1975), 49-59

  19. "The universal group cover of a pro-affine algebraic group", Duke J. Math. 42(1975), 43-49

  20. "The Picard sequence of a fibration", Proc. Amer. Math. Soc. 54(1975), 37-40

  21. "Left algebraic groups", J. of Algebra 35(1975), 253-272

  22. "Projective extensions of Banach algebras", Proc. Amer. Math. Soc. 54(1976), 154-156

  23. "Analytic left algebraic groups", Amer. J. Math. 99(1977),  1045-1059

  24. "Covering spaces of algebraic groups", Amer. Math. Monthly  93(1976), 614-621

  25. "Fundamental, Picard, and divisor class groups of rings of  invariants", Canadian. J. Math. 28(1976), 659-664

  26. "Finite generation of class groups of rings of invariants",  Proc. Amer. Math. Soc. 60(1976), 45-48

  27. "Proper Ga-actions", (with A. Fauntleroy), Duke J. Math.  43(1976), 723-729

  28. "Factorality in quotients of linear Gm-actions", Rocky Mt.  Journal 7(1977), 675-681

  29. "Separately algebraic group laws", Amer. J. Math.  100(1978), 407-409

  30. "Analytic left algebraic groups , II", Trans. Amer. Math.  Soc. 238(1978), 165-177

  31. "Picard sequence of a fibration", Brauer Groups Evanston  1975, Lecture Notes in Mathematics #549, Springer-Verlag, New  York, 1976, 71-85

  32. "Quasi-affine surfaces with Ga-action", (with A.  Fauntleroy), Proc. Amer. Math. Soc. 71(1978), 164-168

  33. "Analytic subgroups of algebraic groups", Duke J. Math.  44(1977), 875-882

  34. "Brauer groups of linear algebraic groups with characters",  Proc. Amer. Math. Soc. 71(1978), 164-168

  35. "Analytic subgroups of algebraic groups, II", Pacific J. Math. 86(1980), 145-154

  36. "Faithfully representable algebraic groups", Copenhagen  Summer Meeting in Algebraic Geometry, Lecture Notes in  Mathematics #732, Springer-Verlag, New York, 1979

  37. "Separated Ga-action", Proc. Amer. Math. Soc. 76(1979),  335-38

  38. "Picard groups of rings of invariants", J. Pure Applied  Algebra 17(1980), 305-311

  39. "Representative functions on simply connected solvable  groups", Amer. J. Math. 102(1980), 303-319

  40. "Moduli for analytic left algebraic groups", Trans. Amer.  Math. Soc. 260(1980), 281-291

  41. "Dimension in rings with solvable algebraic group action",  Math. Scand. 47(1980), 21-28

  42. "Lie algebras with the same modules", Ill. J. Math.  25(1981), 611-621

  43. "Cohomology of unipotent and pro-unipotent groups" (with A.  Lubotzky), J. of Algebra 74(1982), 76-95

  44. "Analytic representations of polycyclic groups", J. of  Algebra 74(1982), 149-158

  45. "Free prounipotent groups" (with A. Lubotzky), J. of  Algebra 80(1983), 323-349

  46. "Unipotent and prounipotent groups: cohomology and  presentations" (with A. Lubotzky), Bull. Amer. Math. Soc.  7(1982), 251-254

  47. "On the primitivity theorem for algebraic groups", Rocky  Mt. Journal 14(1984), 655-660

  48. "Cohomology, Poincare series, and group algebras of  unipotent groups" (with A. Lubotzky), Amer. J. Math. 107(1985),  531-553

  49. "Coordinate rings of prounipotent groups", J. of Algebra  95(1985), 46-58

  50. "Varieties of representations of finitely generated groups"  (with A. Lubotzky), Mem. Amer. Math. Soc. 336(1985), xii+117  pages

  51. "Cohomology of rings with algebraic group action", Advances  in Math. 59(1986), 124-151

  52. "Relation modules of prounipotent groups", J. of Algebra  109(1987), 52-68

  53. "Equivariant completions of rings with reductive group  action, J. Pure Applied Algebra 49(1987), 173-185

  54. "Local structure of representation varieties", Israel J.  Math 62(1988), 326-340

  55. "Local structure of representation varieties: examples"  (with A. Lubotzky), in Geometry of Group Representations,  Contemp. Math. 74(1988), 215-235

  56. "Equvariant completions of affine varieties with reductive  group action", in Invariant Theory, Contemp. Math 88(1989), 1-10

  57. "Simple representations of the integral Heisenberg group"  (With C. Nunley), in Classical Groups and Related Topics, Contemp.  Math. 82(1989), 79-87

  58. "Deformations of representations of discrete groups",  ibid., 89-96

  59. "Equivariant completions and tensor products", in Group Actions  and Invariant Theory, CMS Conference Proceedings 10(1989), 133-136

  60. "Tangential linear representations of automorphism groups of  free groups", Ulam Quart. 1(1992), 50-57

  61. "Every G-module is a submodule of a direct sum of cyclics"  Proc. Amer. Math. Soc. 116(1992), 929-937

  62. "Identities for prounipotent groups", Proceedings of Symposia in  Pure Mathematics 56(1994), 281-289

  63. "Adjoining idempotents" in Rings, Extensions, and Cohomology,   Lecture Notes in Pure and Applied Mathematics #159, Marcel Dekker Inc.,  New York, 1994, 155-163

  64. "Direct limits of finite products of fields", in Zero Dimensional  Commutative Rings, Lecture Notes in Pure and Applied Mathematics #171,   Marcel Dekker Inc., New York ,1995, 299-305

  65. "The Oklahoma Graphing Calculator Project" (with S. Gay), Mathematics  Teacher 89(1996), 362-363

  66. "A note on the Galois correspondence for commutative rings" (with  A. Carboni and G. Janelidze), J. of Algebra 183(1996), 266-272

  67. "Small infinite dimensional modules for algebraic groups", Proc.  Amer. Math. Soc. 125(1997), 75-81

 68. "Square roots", in World Book, Chicago 1998, Volume S, 812

 69. "Lower bounds for dimensions of representation varieties", Trans. Amer. Math. Soc. 350(1998), 4609-4621

 70. "Prounipotent prolongation of algebraic groups", in Recent Progress in Algebra, 
Contemp. Math 224(1999), 169-187

 71. "Deformations of representations", in Algebra, K-Theory, Groups and Education,
Contemp. Math 243(1999), 129-143

 72.  "Differential Galois Theory", NOTICES Amer. Math. Soc. 46(1999), 1041-1049

 73.  "Deformations and liftings of representations", in Combinatorial and Computational 
Algebra, Contemp. Math 264(2000), 3-21 (with E. Aljadeff)

 74.  "The Picard--Vessiot antiderivative closure, Journal of Algebra 244(2001), 1-18

 75.  "Provarieties and observable subgroups of pro--affine algebraic groups, 
Journal of Group Theory" Journal of Group Theory 5(2002), 59-74 (with N. Nahlus)

 76.  "Inverse differential Galois theory", in L. Guo et al, Differential Algebra and Related Topics, World Scientific, New Jersey, 2002, 151-169

 77.  "On the proalgebraic completion of a finitely generated group", Contemp. Math. 296(2002), 171-181

 78.  "Differential Galois Theory",  in  G. Pilz and A. Mikalev, The Concise Handbook of Algebra, Kluwer Academic Publishers, Dordrecht, 2002, 366-369

 79.  "The Picard--Vessiot closure in differential Galois theory", in Banach Center Publications 58, Polish Academy of Sciences, Warsaw, 2002 151-164

 80.  "The proalgebraic completion of rigid groups", Geometricae Dedicata 95(2002) 19-58  (with H. Bass, A. Lubotzky, S. Mozes)

 81 "Universal covers and category theory in polynomial and differential Galois theory", in Galois theory, Hopf algebras, and semiabelian categories, Fields Inst. Commun., 43(2004), 373—385

 82. "Generic rings for Picard–Vessiot extensions and generic differential equations", J. Pure and Applied Algebra 209(2007), 793-800 (with Lourdes Juan)

 83. "On deformations of crossed products”, J. Pure and Applied Algebra 210 (2007), 81-91 (with Eli Aljadeff and Yuval Ginosaur) 

 84. "Differential central simple algebras and Picard-Vessiot representations", Proc. AMS 136 (2008), 1911-1915 (with Lourdes Juan)

 85. "Picard—Vessiot extensions with specified Galois group", Pacific J Math 243 (2009), 233-242 (with Ted Chinburg and Lourdes Juan)

 86. "Differential `Galois’ Extensions with New Constants", C.R. Acad. Sci. Paris, Ser. I  348 (2010) pp. 487-490 (with Lourdes Juan)

 87. "Base change for Picard-Vessiot closures", in  Algebraic methods in dynamical systems, 233–238, Banach Center Publ., 94, Polish Acad. Sci. Inst. Math., Warsaw, 2011. 

 88.  "Differential étale extensions and differential modules over differential rings",  Adv. in Appl. Math. 72 (2016), 195-214.

 89. "Differential projective modules over differential rings", Comm. in Alg. 47(2019) 4336-4346

 90. "Differential projective modules over differential rings, II", Comm. in Alg. 50(2022) 3803-3815

 91. "The differential Galois group of the maximal prounipotent extension is free", Proc. Amer. Math. Soc. 150 (2022) 1421-1433.

 92. "Differential Brauer monoids", Proc. Amer. Math. Soc. Ser, B 10 (2023) 153-165

   



                             BOOKS

          THE SEPARABLE GALOIS THEORY OF COMMUTATIVE RINGS,
  Marcel Dekker, Inc., New York, 1974 xvii+134 pages
 Second edition, revised and corrected, Pure and Applied Mathematics (Boca Raton). CRC Press, Boca Raton, FL, 2014. xvi+168 pp. 

          MODULE CATEGORIES OF ANALYTIC GROUPS, Cambridge Tracts
  in Mathematics vol. 81, Cambridge University Press, Cambridge,
  1982, x+134 pages

          APPLIED MATRIX MODELS: A SECOND COURSE IN LINEAR
  ALGEBRA WITH COMPUTER APPLICATIONS, Wiley, New York, 1985,
  vii+240 pages

	  LECTURES ON DIFFERENTIAL GALOIS THEORY, University Lecture
  Series, Volume 7, American Mathematical Society, Providence, 1994
  xiii+105 pages

          MATHEMATICS EDUCATION RESEARCH: A GUIDE FOR THE RESEARCH MATHEMATICIAN, 
  American Mathematical Society, Providence, 2000, xi+106 pages (with C. 
  McKnight, T. J. Murphy, and M. McKnight) 

                        PROCEEDINGS EDITED

          RING THEORY: PROCEEDINGS OF THE OKLAHOMA CONFERENCE,
  (with B. McDonald and K. Smith), Lecture Notes in Pure and
  Applied Math 7, Marcel Dekker, Inc., New York, 1974

          GEOMETRY OF GROUP REPRESENTATIONS:PROCEEDINGS OF A
  SUMMER RESEARCH CONFERENCE HELD JULY 5-11, 1987, (with W.
  Goldman) Contemporary Math 74, American Mathematical Society,
  Providence, 1988

          RINGS, EXTENSIONS, AND COHOMOLOGY, Lecture Notes in Pure
  and Applied Math 159, Marcel Dekker, Inc., New York 1994

        ALGEBRA, K-THEORY, GROUPS, AND EDUCATION, (with T. Y. Lam), 
Contemporary Math 243, American Mathematical Society, Providence 1999

                       ACCEPTED for PUBLICATION

The Complete Picard-Vessiot Closure, DARTII Proceedings (to appear)