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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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Book Review

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MathSciNet review: 1567131
Full text of review: PDF   This review is available free of charge.
Book Information:

Author: Donald S. Passman
Title: The algebraic structure of group rings
Additional book information: John Wiley & Sons, New York, London, Sydney, Toronto, 1977, xiv + 720 pp., $34.95.

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  • S. A. Amitsur, The radical of field extensions, Bull. Res. Council Israel Sect. F 7F (1957/58), 1–10. MR 103912
  • S. A. Amitsur, On the semi-simplicity of group algebras, Michigan Math. J. 6 (1959), 251–253. MR 108540
  • S. A. Amitsur, Groups with representations of bounded degree. II, Illinois J. Math. 5 (1961), 198–205. MR 122893
  • George M. Bergman, The logarithmic limit-set of an algebraic variety, Trans. Amer. Math. Soc. 157 (1971), 459–469. MR 280489, DOI 10.1090/S0002-9947-1971-0280489-8
  • S. D. Berman, Group algebras of countable abelian $p$-groups, Publ. Math. Debrecen 14 (1967), 365–405 (Russian). MR 225897
  • A. A. Bovdi, Group rings of torsion-free groups, Sibirsk. Mat. Ž. 1 (1960), 555–558 (Russian). MR 0130919
  • R. Brauer and C. Nesbitt, On the modular characters of groups, Ann. of Math. (2) 42 (1941), 556–590. MR 4042, DOI 10.2307/1968918
  • Kenneth A. Brown, On zero divisors in group rings, Bull. London Math. Soc. 8 (1976), no. 3, 251–256. MR 414616, DOI 10.1112/blms/8.3.251
  • Ian G. Connell, On the group ring, Canadian J. Math. 15 (1963), 650–685. MR 153705, DOI 10.4153/CJM-1963-067-0
  • Charles W. Curtis and Irving Reiner, Representation theory of finite groups and associative algebras, Pure and Applied Mathematics, Vol. XI, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1962. MR 0144979
  • Everett C. Dade, Deux groupes finis distincts ayant la même algèbre de groupe sur tout corps, Math. Z. 119 (1971), 345–348 (French). MR 280610, DOI 10.1007/BF01109886
  • Daniel Farkas, Self-injective group algebras, J. Algebra 25 (1973), 313–315. MR 313300, DOI 10.1016/0021-8693(73)90049-5
  • Daniel R. Farkas and D. S. Passman, Primitive Noetherian group rings, Comm. Algebra 6 (1978), no. 3, 301–315. MR 469961, DOI 10.1080/00927877808822247
  • Daniel R. Farkas and Robert L. Snider, Group algebras whose simple modules are injective, Trans. Amer. Math. Soc. 194 (1974), 241–248. MR 357475, DOI 10.1090/S0002-9947-1974-0357475-5
  • Daniel R. Farkas and Robert L. Snider, $K_{0}$ and Noetherian group rings, J. Algebra 42 (1976), no. 1, 192–198. MR 422327, DOI 10.1016/0021-8693(76)90036-3
  • Edward Formanek, Idempotents in Noetherian group rings, Canadian J. Math. 25 (1973), 366–369. MR 316494, DOI 10.4153/CJM-1973-037-6
  • Edward Formanek, Group rings of free products are primitive, J. Algebra 26 (1973), 508–511. MR 321964, DOI 10.1016/0021-8693(73)90011-2
  • Edward Formanek, The zero divisor question for supersolvable groups, Bull. Austral. Math. Soc. 9 (1973), 69–71. MR 325670, DOI 10.1017/S000497270004288X
  • Edward Formanek and Robert L. Snider, Primitive group rings, Proc. Amer. Math. Soc. 36 (1972), 357–360. MR 308178, DOI 10.1090/S0002-9939-1972-0308178-8
  • Enzo R. Gentile, A note on injective group rings, Proc. Amer. Math. Soc. 23 (1969), 431–432. MR 245693, DOI 10.1090/S0002-9939-1969-0245693-X
  • Alfred W. Goldie, The structure of Noetherian rings, Lectures on rings and modules (Tulane Univ. Ring and Operator Theory Year, 1970-1971, Vol. I), Lecture Notes in Math., Vol. 246, Springer, Berlin, 1972, pp. 213–321. MR 0393118
  • J.-M. Goursaud, Sur les anneaux de groupes semi-parfaits, Canadian J. Math. 25 (1973), 922–928 (French). MR 338054, DOI 10.4153/CJM-1973-098-1
  • Jean-Marie Goursaud and Jacques Valette, Sur l’enveloppe injective des anneaux de groupes réguliers, Bull. Soc. Math. France 103 (1975), no. 1, 91–102 (French). MR 379569
  • P. Hall, Finiteness conditions for soluble groups, Proc. London Math. Soc. (3) 4 (1954), 419–436. MR 72873, DOI 10.1112/plms/s3-4.1.419
  • P. Hall, On the finiteness of certain soluble groups, Proc. London Math. Soc. (3) 9 (1959), 595–622. MR 110750, DOI 10.1112/plms/s3-9.4.595
  • B. Hartley, The residual nilpotence of wreath products, Proc. London Math. Soc. (3) 20 (1970), 365–392. MR 258966, DOI 10.1112/plms/s3-20.3.365
  • B. Hartley, Injective modules over group rings, Quart. J. Math. Oxford Ser. (2) 28 (1977), no. 109, 1–29. MR 435127, DOI 10.1093/qmath/28.1.1
  • K. A. Hirsch, On infinite soluble groups. III, Proc. London Math. Soc. (2) 49 (1946), 184–194. MR 17281, DOI 10.1112/plms/s2-49.3.184
  • I. M. Isaacs and D. S. Passman, Groups with representations of bounded degree, Canadian J. Math. 16 (1964), 299–309. MR 167539, DOI 10.4153/CJM-1964-029-5
  • I. M. Isaacs and D. S. Passman, A characterization of groups in terms of the degrees of their characters, Pacific J. Math. 15 (1965), 877–903. MR 191972
  • Gerald J. Janusz, Algebraic number fields, Pure and Applied Mathematics, Vol. 55, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1973. MR 0366864
  • Arun Vinayak Jategaonkar, Integral group rings of polycyclic-by-finite groups, J. Pure Appl. Algebra 4 (1974), 337–343. MR 344345, DOI 10.1016/0022-4049(74)90013-9
  • S. A. Jennings, The structure of the group ring of a $p$-group over a modular field, Trans. Amer. Math. Soc. 50 (1941), 175–185. MR 4626, DOI 10.1090/S0002-9947-1941-0004626-6
  • S. A. Jennings, The group ring of a class of infinite nilpotent groups, Canadian J. Math. 7 (1955), 169–187. MR 68540, DOI 10.4153/CJM-1955-022-5
  • Irving Kaplansky, Rings with a polynomial identity, Bull. Amer. Math. Soc. 54 (1948), 575–580. MR 25451, DOI 10.1090/S0002-9904-1948-09049-8
  • Michel Lazard, Sur les groupes nilpotents et les anneaux de Lie, Ann. Sci. Ecole Norm. Sup. (3) 71 (1954), 101–190 (French). MR 0088496
  • Jacques Lewin, A note on zero divisors in group-rings, Proc. Amer. Math. Soc. 31 (1972), 357–359. MR 292957, DOI 10.1090/S0002-9939-1972-0292957-X
  • A. I. Mal′cev, On the embedding of group algebras in division algebras, Doklady Akad. Nauk SSSR (N.S.) 60 (1948), 1499–1501 (Russian). MR 0025457
  • A. I. Mal′cev, On some classes of infinite soluble groups, Mat. Sbornik N.S. 28(70) (1951), 567–588 (Russian). MR 0043088
  • 40.
    M. Malliavin, Sur les anneaux de groupes FP self-infectifs, C. R. Acad. Sci. Paris 273 (1971), 88-91. MR 44 #5386.
  • Warren May, Commutative group algebras, Trans. Amer. Math. Soc. 136 (1969), 139–149. MR 233903, DOI 10.1090/S0002-9947-1969-0233903-9
  • Donald S. Passman, Infinite group rings, Pure and Applied Mathematics, vol. 6, Marcel Dekker, Inc., New York, 1971. MR 0314951
  • B. H. Neumann, On ordered division rings, Trans. Amer. Math. Soc. 66 (1949), 202–252. MR 32593, DOI 10.1090/S0002-9947-1949-0032593-5
  • Masaru Osima, Notes on blocks of group characters, Math. J. Okayama Univ. 4 (1955), 175–188. MR 78364
  • D. S. Passman, Nil ideals in group rings, Michigan Math. J. 9 (1962), 375–384. MR 144930
  • Donald S. Passman, Infinite group rings, Pure and Applied Mathematics, vol. 6, Marcel Dekker, Inc., New York, 1971. MR 0314951
  • D. S. Passman, Primitive group rings, Pacific J. Math. 47 (1973), 499–506. MR 332942
  • D. S. Passman, Group rings satisfying a polynomial identity, J. Algebra 20 (1972), 103–117. MR 285631, DOI 10.1016/0021-8693(72)90091-9
  • D. S. Passman, Group rings satisfying a polynomial identity. III, Proc. Amer. Math. Soc. 31 (1972), 87–90. MR 289671, DOI 10.1090/S0002-9939-1972-0289671-3
  • D. S. Passman, A new radical for group rings?, J. Algebra 28 (1974), 556–572. MR 427363, DOI 10.1016/0021-8693(74)90060-X
  • D. S. Passman, Advances in group rings, Israel J. Math. 19 (1974), 67–107. MR 357477, DOI 10.1007/BF02756627
  • D. S. Passman, What is a group ring?, Amer. Math. Monthly 83 (1976), no. 3, 173–185. MR 390033, DOI 10.2307/2977018
  • D. S. Passman, The Jacobson radical of a group ring of a locally solvable group, Proc. London Math. Soc. (3) 38 (1979), no. 1, 169–192. MR 520978, DOI 10.1112/plms/s3-38.1.169
  • Sam Perlis and Gordon L. Walker, Abelian group algebras of finite order, Trans. Amer. Math. Soc. 68 (1950), 420–426. MR 34758, DOI 10.1090/S0002-9947-1950-0034758-3
  • Edward C. Posner, Prime rings satisfying a polynomial identity, Proc. Amer. Math. Soc. 11 (1960), 180–183. MR 111765, DOI 10.1090/S0002-9939-1960-0111765-5
  • Guy Renault, Sur les anneaux de groupes, C. R. Acad. Sci. Paris Sér. A-B 273 (1971), A84–A87 (French). MR 288189
  • J. E. Roseblade, Group rings of polycyclic groups, J. Pure Appl. Algebra 3 (1973), 307–328. MR 332944, DOI 10.1016/0022-4049(73)90034-0
  • J. E. Roseblade and P. F. Smith, A note on hypercentral group rings, J. London Math. Soc. (2) 13 (1976), no. 1, 183–190. MR 399146, DOI 10.1112/jlms/s2-13.1.183
  • Alan Rosenberg, On the primitivity of the group algebra, Canadian J. Math. 23 (1971), 536–540. MR 286836, DOI 10.4153/CJM-1971-057-8
  • Jean-Pierre Serre, Cohomologie des groupes discrets, Prospects in mathematics (Proc. Sympos., Princeton Univ., Princeton, N.J., 1970) Ann. of Math. Studies, No. 70, Princeton Univ. Press, Princeton, N.J., 1971, pp. 77–169 (French). MR 0385006
  • Martha Smith, Group algebras, J. Algebra 18 (1971), 477–499. MR 277625, DOI 10.1016/0021-8693(71)90078-0
  • P. F. Smith, On the intersection theorem, Proc. London Math. Soc. (3) 21 (1970), 385–398. MR 294382, DOI 10.1112/plms/s3-21.3.385
  • P. F. Smith, Localization in group rings, Proc. London Math. Soc. (3) 22 (1971), 69–90. MR 294384, DOI 10.1112/plms/s3-22.1.69
  • Jacques Valette, Anneaux de groupes semi-parfaits, C. R. Acad. Sci. Paris Sér. A-B 275 (1972), A1219–A1222 (French). MR 308275
  • Orlando E. Villamayor, On the semisimplicity of group algebras, Proc. Amer. Math. Soc. 9 (1958), 621–627. MR 98769, DOI 10.1090/S0002-9939-1958-0098769-7
  • Orlando E. Villamayor, On weak dimension of algebras, Pacific J. Math. 9 (1959), 941–951. MR 108527
  • R. Walker, Local rings and normalizing sets of elements, Proc. London Math. Soc. (3) 24 (1972), 27–45. MR 294399, DOI 10.1112/plms/s3-24.1.27
  • 68.
    A. Whitcomb, The group ring problem, Ph.D. Thesis, Univ. of Chicago, 1967.
  • S. M. Woods, On perfect group rings, Proc. Amer. Math. Soc. 27 (1971), 49–52. MR 271247, DOI 10.1090/S0002-9939-1971-0271247-4
  • A. E. Zalesskiĭ, The group algebras of solvable groups, Vescī Akad. Navuk BSSR Ser. Fīz.-Mat. Navuk 1970 (1970), no. 2, 13–21 (Russian). MR 0289675
  • 71.
    A. E. Zalesskiĭ, On a problem of Kaplansky, Soviet Math. 13 (1972), 449-452. MR 45 #6947.
    72.
    A. E. Zalesskiĭ, On the semisimplicity of a modular group algebra of a solvable group, Soviet Math. 14 (1973), 101-105.
  • A. E. Zalesskiĭ and A. V. Mihalev, Group rings, Current problems in mathematics, Vol. 2 (Russian), Akad. Nauk SSSR Vsesojuz. Inst. Naučn. i Tehn. Informacii, Moscow, 1973, pp. 5–118. (errata insert) (Russian). MR 0414623

  • Review Information:

    Reviewer: D. A. R. Wallace
    Journal: Bull. Amer. Math. Soc. 1 (1979), 402-410
    DOI: https://doi.org/10.1090/S0273-0979-1979-14616-0