Donald S. Passman: Publications

Books

  1. Permutation Groups, Benjamin, New York, (1968), [Dover, Mineola, (2012)].
  2. Infinite Group Rings, Marcel Dekker, New York, (1971).
  3. The Algebraic Structure of Group Rings, Wiley-Interscience, New York (1977), [Krieger, Malabar, (1985)], [Dover, Mineola, (2011)].
  4. Group rings, Crossed Products and Galois Theory, CBMS Conference Notes, AMS, Providence, 1986.
  5. Infinite Crossed Products, Academic Press, Boston, (1989), [Dover, Mineola, (2013)].
  6. A Course in Ring Theory, Wadsworth, Pacific Grove, (1991), [Chelsea-AMS, Providence, (2004)].
  7. Lectures on Linear Algebra, World Scientific, Singapore, (2022).

Articles

  1. Nil ideals in group rings, Michigan Math. J. 9 (1962), 374-384.
  2. On groups with enough finite representations, Proc. AMS 14 (1963), 782-797.
  3. Groups with representations of bounded degree, (with I. M. Isaacs) Canadian J. Math. 16 (1964), 299-309.
  4. Groups whose irreducible representations have degrees dividing p^e, (with I. M. Isaacs) Illinois J. Math. 8 (1964), 446-457.
  5. The group algebras of groups of order p^4 over a modular field, Michigan Math. J. 12 (1965), 405-415.
  6. Isomorphic groups and group rings, Pacific J. Math. 15 (1965), 561-583. (ibid. 43 (1972), 823-824).
  7. A characterization of groups in terms of the degrees of their characters, (with I. M. Isaacs) Pacific J. Math. 15 (1965), 877-903.
  8. Groups whose irreducible representations have degrees dividing p^2, Pacific J. Math. 17 (1966), 475-496.
  9. Character kernels of discrete groups, Proc. AMS 17 (1966), 487-492.
  10. A note on the action of p-groups on abelian groups, Proc. AMS 17 (1966), 915-921.
  11. Groups with normal, solvable Hall p'-subgroups, Trans. AMS 123 (1966), 99-111.
  12. Generalized Frobenius complements, (with B. Lou) Proc. AMS 17 (1966), 1166-1172.
  13. Half-transitive automorphism groups, (with I. M. Isaacs) Canadian J. Math. 18 (1966), 1243-1250.
  14. Solvable half-transitive automorphism groups, J. Algebra 6 (1967), 285-304.
  15. Solvable 3/2-transitive permutation groups, J. Algebra 7 (1967), 192-207.
  16. A characterization of groups in terms of the degrees of their characters II, (with I. M. Isaacs) Pacific J. Math. 24 (1968), 467-510.
  17. Groups with relatively few nonlinear irreducible characters, (with I. M. Isaacs) Canadian J. Math. 20 (1968), 1451-1458.
  18. On the semisimplicity of modular group algebras, Proc. AMS 20 (1969), 515-519.
  19. p-Solvable doubly transitive permutation groups, Pacific J. Math. 26 (1968), 555-577.
  20. Some 5/2-transitive permutation groups, Pacific J. Math. 28 (1969), 157-171.
  21. Blocks and normal subgroups, J. Algebra 12 (1969), 569-575.
  22. Central idempotents in group rings, Proc. AMS 22 (1969), 555-556.
  23. Finite groups with small character degrees and large prime divisors II, (with I. M. Isaacs) Pacific J. Math. 29 (1969), 311-324.
  24. Exceptional 3/2-transitive permutation groups, Pacific J. Math. 29 (1969), 669-713.
  25. On the semisimplicity of modular group algebras II, Canadian J. Math. 21 (1969), 1137-1145.
  26. Radicals of twisted group rings, Proc. London Math. Soc. 20 (1970), 409-437.
  27. On the semisimplicity of twisted group algebras, Proc. AMS 25 (1970), 161-166.
  28. Units in modular group rings, (with D. B. Coleman) Proc. AMS 25 (1970), 510-512.
  29. Nonnormal subgroups of p-groups, J. Algebra 15 (1970), 352-370.
  30. Twisted group algebras of discrete groups, Proc. London Math. Soc. 21 (1970), 219-231.
  31. Radicals of twisted group rings II, Proc. London Math. Soc. 22 (1971), 633-651.
  32. Linear identities in group rings, Pacific J. Math. 36 (1971), 457-483.
  33. Linear identities in group rings II, Pacific J. Math. 36 (1971), 485-505.
  34. Idempotents in group rings, Proc. AMS 28 (1971), 371-374.
  35. Group rings of infinite groups, Proc. Symposia in Pure Math. 21 (1971), 117-122.
  36. Group rings satisfying a polynomial identity, J. Algebra 20 (1972), 103-117.
  37. Group rings satisfying a polynomial identity II, Pacific J. Math. 39 (1971), 425-438.
  38. Minimal ideals in group rings, Proc. AMS 31 (1972), 81-86.
  39. Group rings satisfying a polynomial identity III, Proc. AMS 31 (1972), 87-90.
  40. Surgery with coefficients in a field, (with T. Petrie) Annals of Math. 95 (1972), 385-405.
  41. The Jacobian of a growth transformation, Pacific J. Math. 44 (1973), 281-290.
  42. On the ring of quotients of a group ring, Proc. AMS 33 (1972), 221-225.
  43. Some isolated subsets of infinite solvable groups, Pacific J. Math. 45 (1973), 313-319.
  44. On the semisimplicity of group rings of solvable groups, (with C. R. Hampton) Trans. AMS 173 (1972), 289-301.
  45. On the semisimplicity of group rings of linear groups, Pacific J. Math. 47 (1973), 221-228.
  46. On the semisimplicity of group rings of linear groups II, Pacific J. Math. 48 (1973), 215-234.
  47. Lie solvable group rings, (with I. B. S. Passi and S. K. Sehgal), Canadian J. Math. 25 (1973), 748-757.
  48. Primitive group rings, Pacific J. Math. 47 (1973), 499-506.
  49. A new radical for group rings?, J. Algebra 28 (1974), 556-572.
  50. The semisimplicity problem for group rings, Symposia Math. 13 (1974), 333-342.
  51. Subnormality in locally finite groups, Proc. London Math. Soc. 28 (1974), 631-653.
  52. Advances in group rings, Israel J. Math. 19 (1974), 67-107.
  53. The type I part of a group ring, Comm. Algebra 2 (1974), 469-473.
  54. Radicals of group rings, Comm. Algebra 2 (1974), 295-305.
  55. Radical ideals in group rings of locally finite groups, J. Algebra 33 (1975), 472-497.
  56. On the semisimplicity of group rings of some locally finite groups, Pacific J. Math. 58 (1975), 179-207.
  57. What is a group ring?, Amer. Math. Monthly 83 (1976), 173-184.
  58. Group rings with simple augmentation ideals, (with K. Bonvallet, B. Hartley and M. K. Smith) Proc. AMS 56 (1976), 79-82.
  59. A mechanism for describing ideals in group rings, Ring Theory, Proceedings of Conference on Noncommutative Rings, Marcel Dekker, New York (1977), 63-69.
  60. Observations on group rings, Comm. Algebra 5 (1977), 1119-1162.
  61. Primitive Noetherian group rings, (with D. R. Farkas) Comm. Algebra 6 (1978), 301-315.
  62. The Jacobson radical of a group ring of a locally solvable group, Proc. London Math. Soc 38 (1979), 169-192. (ibid. 39 (1979), 208-210).
  63. Centers and prime ideals in group algebras of polycyclic-by-finite groups, (with M. Lorenz) J. Algebra 57 (1979), 355-386.
  64. Crossed products over prime rings, (with S. Montgomery) Israel J. Math. 31 (1978), 224-256.
  65. Crossed products over semiprime rings, Houston J. Math. 4 (1978), 583-592.
  66. Prime ideals in crossed products of finite groups, (with M. Lorenz) Israel J. Math. 33 (1979), 89-132.
  67. The radical of the center of a group algebra, Proc. AMS. 78 (1980), 323-326.
  68. Integrality and normalizing extensions of rings, (with M. Lorenz) J. Algebra 61 (1979), 289-297.
  69. Observations on crossed products and fixed rings, (with M. Lorenz) Comm. Algebra 8 (1980), 743-779.
  70. Prime ideals in group algebras of polycyclic-by-finite groups, (with M. Lorenz) Proc. London Math. Soc. 43 (1981), 520-543.
  71. Two applications of Maschke's theorem, (with M. Lorenz), Comm. Algebra 8 (1980), 1853-1866.
  72. Addendum-Prime ideals in crossed products of finite groups, (with M. Lorenz) Israel J. Math. 35 (1980), 311-322.
  73. Nonexistence of partial traces for group actions, (with R. M. Guralnick and I. M. Isaacs) Rocky Mt. J. 11 (1981), 395-405.
  74. Units in integral group rings, (with P. F. Smith) J. Algebra 69 (1981), 213-239.
  75. Fixed rings and integrality, J. Algebra 68 (1981), 510-519.
  76. X-Inner automorphisms of group rings, (with S. Montgomery) Houston J. Math. 7 (1981), 395-402.
  77. Prime ideals in normalizing extensions, J. Algebra 73 (1981), 556-572.
  78. Universal fields of fractions for polycyclic group algebras, Glasgow Math. J. 23 (1982), 103-113.
  79. X-Inner automorphisms of group rings II, (with S. Montgomery) Houston J. Math. 8 (1982), 537-544.
  80. Nil ideals of bounded degree in group rings, Comm. Algebra 10 (1982), 1487-1495.
  81. It's essentially Maschke's theorem, Rocky Mt. J. 13 (1983), 37-54.
  82. Semiprime and prime crossed products, J. Algebra 83 (1983), 158-178.
  83. Galois theory of prime rings, (with S. Montgomery) J. Pure and Appl. Algebra 31 (1984), 139-184.
  84. Outer Galois theory of prime rings, (with S. Montgomery) Rocky Mt. J. 14 (1984), 305-318.
  85. Group rings of polycyclic groups, in "Group Theory: essays for Philip Hall", Academic Press, London, 1984, pp. 207-257.
  86. The strongly prime radical of crossed products, (with M. M. Parmenter and P. N. Stewart) Comm. Algebra 12 (1984), 1099-1113.
  87. Infinite crossed products and group-graded rings, Trans. AMS 284 (1984), 707-727.
  88. Cancellative group-graded rings, in "Methods in Ring Theory", Reidel, 1984, pp. 403-414.
  89. Semiprime crossed products, Houston J. Math. 11 (1985), 257-268.
  90. On the Goldie rank of group algebras, Comm. Algebra 13 (1985), 1305-1312.
  91. Algebraic crossed products, Contemporary Math. 43 (1985), 209-225.
  92. X-Inner automorphisms of crossed products and semi-invariants of Hopf algebras, (with S. Montgomery) Israel J. Math. 55 (1986), 33-57.
  93. Computing the symmetric ring of quotients, J. Algebra 105 (1987), 207-235.
  94. Prime ideals in enveloping rings, Trans. AMS 302 (1987), 535-560.
  95. Prime ideals in polycyclic crossed products, Trans. AMS 301 (1987), 737-759.
  96. Radicals of crossed products of enveloping algebras, (with J. Bergen and S. Montgomery) Israel J. Math. 59 (1987), 167-184.
  97. Prime ideals in fixed rings of free algebras, (with S. Montgomery) Comm. Algebra 15 (1987), 2209-2234.
  98. Algebraic analogs of the Connes spectrum, (with S. Montgomery) J. Algebra 115 (1988), 92-124.
  99. Prime ideals in restricted enveloping rings, Comm. Algebra 16 (1988), 1411-1436.
  100. The structure of G_0 for certain polycyclic group algebras and related algebras, (with M. Lorenz) Contemporary Math. 93 (1989), 283-302.
  101. X-inner automorphisms of enveloping rings, (with J. Osterburg) J. Algebra 130 (1990), 277-312.
  102. Delta methods in enveloping rings, (with J. Bergen) J. Algebra 133 (1990), 277-312.
  103. Enveloping algebras satisfying a polynomial identity, J. Algebra 134 (1990), 469-490.
  104. Crossed products and enveloping algebras satisfying a polynomial identity, Israel Math. Conf. Proc. (1989), 61-73.
  105. Algebraic elements in group rings, (with I. Passi) Proc. AMS 108 (1990), 871-877.
  106. Skew group rings and free rings, J. Algebra 131 (1990), 502-512.
  107. Delta methods in enveloping algebras of Lie superalgebras, (with J. Bergen) Trans. AMS 334 (1992), 259-280.
  108. Prime ideals in crossed products, in "Noncommutative Rings", MSRI Publ. 24 (1992), 99-113.
  109. What makes a skew group ring prime?, (with J. Osterburg) in "Azumaya Algebras, Actions, and Modules", Contemporary Math. 124 (1992), 165-177.
  110. A Connes spectrum for Hopf algebras, (with J. Osterburg and D. Quinn) Contemporary Math. 130 (1992), 311-334.
  111. Delta methods in enveloping rings II, (with J. Bergen) J. Algebra, 156 (1993), 494-534.
  112. Computing the Connes spectrum of a Hopf algebra, (with J. Osterburg) Israel J. Math. 80 (1992), 225-253.
  113. The adjoint representation of group algebras and enveloping algebras, Publicacions Mathematiques 36 (1992), 861-878.
  114. Delta methods in enveloping algebras of Lie superalgebras II, (with J. Bergen) J. Algebra 166 (1994), 568-610.
  115. Semiprimitivity of group algebras of locally finite simple groups, (with A. E. Zalesskii) Proc. London Math. Soc. 67 (1993) 243-276.
  116. Semiprimitivity of group algebras of locally finite groups, in "Infinite Groups and Group Rings", World Scientific, Singapore, 1993, pp. 77-101.
  117. Chains of primitive ideals, Contemporary Math. 169 (1994) 475-480.
  118. Semiprimitivity of group algebras of infinite simple groups of Lie type, Proc. AMS 121 (1994) 399-403.
  119. The (almost) right Connes spectrum, in "Advances in Hopf Algebras", Dekker, New York, 1994, pp. 187-203.
  120. Burnside's theorem for Hopf algebras, (with D. Quinn) Proc. AMS, 123 (1995), 327-333.
  121. Involutory Hopf algebras, (with D. Quinn) Trans. AMS, 347 (1995), 2657-2668.
  122. Semiprimitivity of group algebras of locally finite groups II, J. Pure Applied Algebra, 107 (1996), 271-302.
  123. Derivations of skew polynomial rings, (with J. M. Osborn), J. Algebra, 176 (1995), 417-448.
  124. Semiprimitivity of group algebras: a survey, Atas da XII Escola de Algebra, IMECC-UNICAMP, 1995, pp. 168-187.
  125. Delta ideals of Lie color algebras, (with J. Bergen), J. Algebra, 177 (1995), 740-754.
  126. The semiprimitivity problem for group algebras of locally finite groups, Israel J. Math., 96 (1996), 481-509.
  127. Representations of the Gupta-Sidki group, (with W. V. Temple), Proc. AMS, 124 (1996), 1403-1410.
  128. The semiprimitivity problem for twisted group algebras of locally finite groups, Proc. London Math. Soc. (3), 73 (1996), 323-357.
  129. Ultraproducts and the group ring semiprimitivity problem, Resenhas IME-USP, 2 (1996), 253-261.
  130. Group algebras whose units satisfy a group identity II, Proc. AMS, 125 (1997), 657-662.
  131. The Jacobson radical of group rings of locally finite groups, Trans. AMS, 349 (1997) 4696-4751.
  132. Construction of free subgroups in the group of units of modular group algebras, (with J. Z. Goncalves), Comm. Algebra, 24 (1996), 4211-4215.
  133. Semiprimitivity of group algebras: past results and recent progress, in "Trends in Ring Theory", Conf. Proc. Canadian Math. Soc. (vol. 22), AMS, Providence, 1997.
  134. Enveloping algebras of Lie color algebras: primeness versus graded-primeness (with J. Bergen), Proc. AMS, 126 (1998), 1623-1635.
  135. Group algebras with units satisfying a group identity II, (with Chia-Hsin Liu), Proc. AMS, 127 (1999), 337-341.
  136. The semiprimitivity of group algebras, in "Methods in Ring Theory", vol. 198, Marcel Dekker, New York, 1998, pp. 199-211.
  137. Semi-invariants and weights of group algebras of finite groups, (with P. Wauters), Proc. AMS, 127 (1999), 1323-1329.
  138. Noetherian down-up algebras, (with Ellen Kirkman and Ian M. Musson), Proc. AMS, 127 (1999), 3161-3167.
  139. Simple Lie algebras of Witt type, J. Algebra, 206 (1998), 682-692.
  140. Simple Lie color algebras of Witt type, J. Algebra, 208 (1998), 698-721.
  141. Groups with all irreducible modules of finite degree, (with W. V. Temple), in "Algebra", de Gruyter, Berlin, 2000, pp. 263--280.
  142. Simple Lie algebras of special type, (with J. Bergen), J. Algebra, 227 (2000), 45-67.
  143. Trace methods in twisted group rings, Proc. AMS, 129 (2001), 943-946.
  144. Unitary units in group algebras, (with J. Z. Goncalves), Israel J. Math., 125 (2001), 131-155.
  145. Invariant ideals of abelian group algebras and representations of groups of Lie type, (with A. E. Zalesskii), Trans. AMS, 353 (2001), 2971-2982.
  146. Invariant ideals of abelian group algebras under the multiplicative action of a field, I, (with A. E. Zalesskii), Proc. AMS, 130 (2002), 939-949.
  147. Invariant ideals of abelian group algebras under the multiplicative action of a field, II, (with J. M. Osterburg and A. E. Zalesskii), Proc. AMS, 130 (2002), 951-957.
  148. Free unit groups in group algebras, (with J. Z. Goncalves), J. Algebra, 246 (2001), 226-252.
  149. Twisted group algebras and generalized polynomial identities, Comm. Algebra, 29 (2001), 3683-3710.
  150. Polycyclic restricted Lie algebras (with V. M. Petrogradsky), Comm. Algebra, 29 (2001), 3829-3838.
  151. Trace methods in twisted group rings, II, (with J. M. Osterburg), Proc. AMS, 130 (2002), 3495-3506.
  152. Invariant ideals and polynomial forms, Trans. AMS, 354 (2002), 3379-3408.
  153. Free unit groups in algebras, (with J. Z. Goncalves), Comm. Algebra, 31 (2003), 2219-2227.
  154. Invariant ideals of abelian group algebras under the action of simple linear groups, Resenhas IME-USP, 5 (2002), 377-390.
  155. Finitely generated simple algebras: a question of B. I. Plotkin, (with A. I. Lichtman), Israel J. Math., 143 (2004), 341-359.
  156. Free products in linear groups, Proc. AMS, 132 (2004), 37-46.
  157. Embedding free products in the unit group of an integral group ring, (with J. Z. Goncalves), Archiv der Mathematik, 82 (2004), 97-102.
  158. Filtrations in semisimple rings, Trans. AMS, 357 (2005), 5051-5066.
  159. Filtrations in semisimple Lie algebras, I, (with Y. Barnea), Trans. AMS, 358 (2006), 1983-2010.
  160. Filtrations in semisimple Lie algebras, II, (with Y. Barnea), Trans. AMS, 360 (2008), 801-817.
  161. Linear groups and group rings, (with J. Z. Goncalves), J. Algebra, 295 (2006), 94-118, (ibid. 307 (2007), 930-931).
  162. Polynomial and inverse forms, Contemporary Math., 420 (2006), 277-288.
  163. Prime Lie rings of derivations of commutative rings in characteristic 2, (with Chia-Hsin Liu), J. Algebra, 311 (2007), no. 1, 352-364.
  164. "Multiplicative Invariant Theory" by Martin Lorenz, (book review), Bull. AMS, 44 (2007), 157-162.
  165. A description of incidence rings of group automata, (with A. V. Kelarev), Contemporary Math., 456 (2008), 27-33.
  166. Free subgroups in linear groups and group rings, Contemporary Math., 456 (2008), 151-164.
  167. Finitary actions and invariant ideals, Turkish J. Math., 31 (2007), 113-130.
  168. Involutions and free pairs of bicyclic units in integral group rings, (with J. Z. Goncalves), J. Group Theory, 13 (2010), 721-742.
  169. Filtrations in semisimple Lie algebras, III, in "Advances in Ring Theory", Birkhauser, Basel (2010), pp. 257-268.
  170. Multiplicative Jordan decomposition in group rings of 3-groups, (with Chia-Hsin Liu), J. Algebra and Applications, 8 (2009), 505-519.
  171. Multiplicative Jordan decomposition in group rings of 2,3-groups, (with Chia-Hsin Liu), J. Algebra and Applications, 9 (2010), 483-492.
  172. Invariant ideals of abelian group algebras under the torus action of a field, I, J. Algebra, 324 (2010), 3035-3043.
  173. Character theory and group rings, Contemporary Math., 524 (2010), 139-148.
  174. Invariant ideals of abelian group algebras under the torus action of a field, II, J. Algebra, 331 (2011), 362-377.
  175. Involutions and free pairs of Bass cyclic units in integral group rings, (with J. Z. Goncalves), J. Algebra and Applications, 10 (2011), 711-725.
  176. Rewritable groups, (with M. I. Elashiry), J. Algebra, 345 (2011), 190-201.
  177. Elementary bialgebra properties of group rings and enveloping rings: An introduction to Hopf algebras, Commun. Algebra, 42 (2014), 2222-2253.
  178. Multiplicative Jordan decomposition in group rings of 3-groups, II, (with Chia-Hsin Liu), Commun. Algebra, 42 (2014), 2633-2639.
  179. Multiplicative Jordan decomposition in group rings with a Wedderburn component of degree 3, (with Chia-Hsin Liu), J. Algebra, 388 (2013), 203-218.
  180. Explicit free groups in division rings (with J. Z. Goncalves), Proc. AMS, 143 (2015), 459-468.
  181. Involutions and free pairs of bicyclic units in integral group rings of non-nilpotent groups, (with J. Z. Goncalves), Proc. AMS, 143 (2015), 2395-2401.
  182. Groups with certain normality conditions, (with Chia-Hsin Liu), Commun. Algebra, 44 (2016), 3308-3323.
  183. Free groups in normal subgroups of the multiplicative group of a division ring (with J. Z. Goncalves), J. Algebra, 440 (2015) 128-144.
  184. Permutational and rewritable groups, Proc. AMS, 147 (2019) 995-1003.
  185. Free pairs of symmetric elements in normal subgroups of division rings (with J. Z. Goncalves), J. Algebra, 550 (2020) 154-185.
  186. Finite presentation (with L. W. Small), Israel J. Math., 244(1) (2021) 185-214.
  187. On the counterexamples to the unit conjecture for group rings, arXiv: 2108.06570v2 [math.RA] 26Aug2021.
  188. Affine Noetherian algebras and extensions of the base field II (with L. W. Small),


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