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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

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.


MathSciNet review: 1567914
Full text of review: PDF   This review is available free of charge.
Book Information:

Author: D. S. Passman
Title: Infinite crossed products
Additional book information: Academic Press, New York, 460 pp., $84.50. ISBN 0-12-546390-1.

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  • A. Adrian Albert and Helmut Hasse, A determination of all normal division algebras over an algebraic number field, Trans. Amer. Math. Soc. 34 (1932), no. 3, 722–726. MR 1501659, DOI 10.1090/S0002-9947-1932-1501659-X
  • S. A. Amitsur, On central division algebras, Israel J. Math. 12 (1972), 408–420. MR 318216, DOI 10.1007/BF02764632
  • Gorô Azumaya, New foundation of the theory of simple rings, Proc. Japan Acad. 22 (1946), no. 11, 325–332. MR 42387
  • A. A. Bovdi, Crossed products of a semigroup and a ring, Dokl. Akad. Nauk SSSR 137 (1961), 1267–1269 (Russian). MR 0132766
    • [BHN] R. Brauer, H. Hasse, and E. Noether, Beweis eines Hauptsatzes in der Theorie der Algebren, J. für Math. 167 (1932), 399-404.

  • M. Cohen and S. Montgomery, Group-graded rings, smash products, and group actions, Trans. Amer. Math. Soc. 282 (1984), no. 1, 237–258. MR 728711, DOI 10.1090/S0002-9947-1984-0728711-4
  • P. M. Cohn, Free rings and their relations, 2nd ed., London Mathematical Society Monographs, vol. 19, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London, 1985. MR 800091
    • [D1] L. E. Dickson, Abstract, Bull. Amer. Math. Soc. (N.S.) 12 (1906), 441-442.

  • L. E. Dickson, Linear associative algebras and abelian equations, Trans. Amer. Math. Soc. 15 (1914), no. 1, 31–46. MR 1500963, DOI 10.1090/S0002-9947-1914-1500963-8
  • George A. Elliott, Automorphisms determined by multipliers on ideals of a $C^*$-algebra, J. Functional Analysis 23 (1976), no. 1, 1–10. MR 0440372, DOI 10.1016/0022-1236(76)90054-9
  • Joe W. Fisher and Susan Montgomery, Semiprime skew group rings, J. Algebra 52 (1978), no. 1, 241–247. MR 480616, DOI 10.1016/0021-8693(78)90272-7
  • Joe W. Fisher and James Osterburg, Some results on rings with finite group actions, Ring theory (Proc. Conf., Ohio Univ., Athens, Ohio, 1976) Lecture Notes in Pure and Appl. Math., Vol. 25, Dekker, New York, 1977, pp. 95–111. MR 0442022
  • N. Jacobson, The fundamental theorem of the Galois theory for quasi-fields, Ann. of Math. (2) 41 (1940), 1–7. MR 1219, DOI 10.2307/1968817
  • Nathan Jacobson, The Theory of Rings, American Mathematical Society Mathematical Surveys, Vol. II, American Mathematical Society, New York, 1943. MR 0008601
  • V. K. Harčenko, The Galois theory of semiprime rings, Algebra i Logika 16 (1977), no. 3, 313–363 (Russian). MR 0573067
  • V. K. Harčenko, Algebras of invariants of free algebras, Algebra i Logika 17 (1978), no. 4, 478–487, 491 (Russian). MR 538309
  • V. K. Kharchenko, Automorphisms and derivations of associative rings, Mathematics and its Applications (Soviet Series), vol. 69, Kluwer Academic Publishers Group, Dordrecht, 1991. Translated from the Russian by L. Yuzina. MR 1174740, DOI 10.1007/978-94-011-3604-4
  • Jakob Levitzki, On normal products of algebras, Ann. of Math. (2) 33 (1932), no. 3, 377–402. MR 1503062, DOI 10.2307/1968521
  • Martin Lorenz and D. S. Passman, Prime ideals in crossed products of finite groups, Israel J. Math. 33 (1979), no. 2, 89–132. MR 571248, DOI 10.1007/BF02760553
  • Martin Lorenz and D. S. Passman, Prime ideals in group algebras of polycyclic-by-finite groups, Proc. London Math. Soc. (3) 43 (1981), no. 3, 520–543. MR 635568, DOI 10.1112/plms/s3-43.3.520
  • Yôichi Miyashita, On Galois extensions and crossed products, J. Fac. Sci. Hokkaido Univ. Ser. I 21 (1970), 97–121. MR 0271163
  • J. C. McConnell and J. C. Robson, Noncommutative Noetherian rings, Pure and Applied Mathematics (New York), John Wiley & Sons, Ltd., Chichester, 1987. With the cooperation of L. W. Small; A Wiley-Interscience Publication. MR 934572
  • Susan Montgomery, Outer automorphisms of semi-prime rings, J. London Math. Soc. (2) 18 (1978), no. 2, 209–220. MR 509936, DOI 10.1112/jlms/s2-18.2.209
  • Susan Montgomery, Fixed rings of finite automorphism groups of associative rings, Lecture Notes in Mathematics, vol. 818, Springer, Berlin, 1980. MR 590245
  • Susan Montgomery, Prime ideals and group actions in noncommutative algebras, Invariant theory (Denton, TX, 1986) Contemp. Math., vol. 88, Amer. Math. Soc., Providence, RI, 1989, pp. 103–124. MR 999986, DOI 10.1090/conm/088/999986
  • John A. Moody, Induction theorems for infinite groups, Bull. Amer. Math. Soc. (N.S.) 17 (1987), no. 1, 113–116. MR 888884, DOI 10.1090/S0273-0979-1987-15527-3
  • Yoshiomi Nakagami and Masamichi Takesaki, Duality for crossed products of von Neumann algebras, Lecture Notes in Mathematics, vol. 731, Springer, Berlin, 1979. MR 546058
  • Tadasi Nakayama and Gorô Azumaya, On irreducible rings, Ann. of Math. (2) 48 (1947), 949–965. MR 24891, DOI 10.2307/1969388
  • Emmy Noether, Nichtkommutative Algebra, Math. Z. 37 (1933), no. 1, 514–541 (German). MR 1545411, DOI 10.1007/BF01474591
  • Donald S. Passman, The algebraic structure of group rings, Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1977. MR 0470211
  • D. S. Passman, Semiprime crossed products, Houston J. Math. 11 (1985), no. 2, 257–267. MR 792201
  • D. S. Passman, Prime ideals in polycyclic crossed products, Trans. Amer. Math. Soc. 301 (1987), no. 2, 737–759. MR 882713, DOI 10.1090/S0002-9947-1987-0882713-9
  • Declan Quinn, Integrality over fixed rings, J. London Math. Soc. (2) 40 (1989), no. 2, 206–214. MR 1044269, DOI 10.1112/jlms/s2-40.2.206
  • Marc A. Rieffel, Actions of finite groups on $C^{\ast }$-algebras, Math. Scand. 47 (1980), no. 1, 157–176. MR 600086, DOI 10.7146/math.scand.a-11882
  • J. E. Roseblade, Prime ideals in group rings of polycyclic groups, Proc. London Math. Soc. (3) 36 (1978), no. 3, 385–447. MR 491797, DOI 10.1112/plms/s3-36.3.385
  • B. L. van der Waerden, A history of algebra, Springer-Verlag, Berlin, 1985. From al-Khwārizmī to Emmy Noether. MR 803326, DOI 10.1007/978-3-642-51599-6
  • J. H. M. Wedderburn, A type of primitive algebra, Trans. Amer. Math. Soc. 15 (1914), no. 2, 162–166. MR 1500970, DOI 10.1090/S0002-9947-1914-1500970-5
    • [Z] A. E. Zaleskiĭ, Irreducible representations of finitely-generated nilpotent torsion-free groups, Math. Notes 9 (1971), 117-123.

  • A. E. Zalesskiĭ and O. M. Neroslavskiĭ, Simple Noetherian rings, Vescī Akad. Navuk BSSR Ser. Fīz.-Mat. Navuk 5 (1975), 38–42, 138 (Russian). MR 0389968
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    Review Information:

    Reviewer: Susan Montgomery
    Journal: Bull. Amer. Math. Soc. 24 (1991), 391-402
    DOI: https://doi.org/10.1090/S0273-0979-1991-16044-1