Israel Journal of Mathematics

, Volume 96, Issue 1, pp ix–xxvii | Cite as

Shimshon Avraham Amitsur (1921 — 1994)

  • Avinoam Mann


American Mathematical Society Commutative Ring English Summary Israel Journal Division Algebra 
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Publications of S.A. Amitsur

  1. 1.
    Applications of the theory of linear differential equations I, Riveon lematematica1 (1946/7), 47–48 (in Hebrew; English summary).Google Scholar
  2. 2.
    Applications of the theory of linear differential equations II, Riveon lematematica1 (1946/7), 79–82 (in Hebrew; English summary).Google Scholar
  3. 3.
    On unique factorization in rings, Riveon lematematica2 (1948), 28–29 (in Hebrew; English summary).Google Scholar
  4. 4.
    A generalization of a theorem on linear differential equations, Bulletin of the American Mathematical Society54 (1948), 937–941zbMATHMathSciNetGoogle Scholar
  5. 5.
    Contributions to the theory of central simple algebras, Summary of thesis submitted to the Hebrew University of Jerusalem, 1949, pp. 1–28.Google Scholar
  6. 6.
    On a lemma of Kaplansky, Riveon lematematica3 (1949), 47–48, 52 (in Hebrew; English summary).MathSciNetGoogle Scholar
  7. 7.
    La representation d’algebres centrales simples, Compte rendus de l’Academie des Science, Paris230 (1950), 902–904.zbMATHMathSciNetGoogle Scholar
  8. 8.
    Construction d’algebres centrales simples sur des corps de caracteristique zero, Compte rendus de l’Academie des Science, Paris230 (1950), 1026–1028.zbMATHMathSciNetGoogle Scholar
  9. 9.
    Minimal identities for algebras (co-author J. Levitzki), Proceedings of the American Mathematical Society1 (1950), 449–463.zbMATHMathSciNetCrossRefGoogle Scholar
  10. 10.
    Finite differential polynomials, Riveon lematematica4 (1950), 1–8 (in Hebrew; English summary).MathSciNetGoogle Scholar
  11. 11.
    Remarks on minimal identities for algebras (co-author J. Levitzki), Proceedings of the American Mathematical Society2 (1951), 320–327.zbMATHMathSciNetCrossRefGoogle Scholar
  12. 12.
    Nil PI-rings, Proceedings of the American Mathematical Society2 (1951), 538–540.zbMATHMathSciNetCrossRefGoogle Scholar
  13. 13.
    Semi-group rings, Riveon lematematica5 (1951), 5–9 (in Hebrew: English summary).MathSciNetGoogle Scholar
  14. 14.
    An embedding of PI-rings, Proceedings of the American Mathematical Society3 (1952), 3–9.zbMATHMathSciNetCrossRefGoogle Scholar
  15. 15.
    A general theory of radicals. I. Radicals in complete lattices, American Journal of Mathematics74 (1952), 774–786.zbMATHMathSciNetCrossRefGoogle Scholar
  16. 16.
    The problem of Kurosh-Levitzki-Jacobson, Riveon lematematica5 (1952), 41–48 (in Hebrew; English summary).MathSciNetGoogle Scholar
  17. 17.
    The identities of PI-rings, Proceedings of the American Mathematical Society4 (1953), 27–34.zbMATHMathSciNetCrossRefGoogle Scholar
  18. 18.
    An electrical computer for the solution of linear simultaneous equations (co-authors A. Many, U. Oppenheim), Review of Scientific Instruments24 (1953), 112–116.MathSciNetCrossRefGoogle Scholar
  19. 19.
    Applications to a polynomial identity, Riveon lematematica7 (1954), 30–32 (in Hebrew; English summary).MathSciNetGoogle Scholar
  20. 20.
    A general theory of radicals. II. Radicals in rings and bicategories, American Journal of Mathematics76 (1954), 100–125.zbMATHMathSciNetCrossRefGoogle Scholar
  21. 21.
    A general theory of radicals. III. Applications, American Journal of Mathematics76 (1954), 126–136.zbMATHMathSciNetCrossRefGoogle Scholar
  22. 22.
    Non-commutative cyclic fields, Duke Mathematical Journal21 (1954), 87–105.zbMATHMathSciNetCrossRefGoogle Scholar
  23. 23.
    Differential polynomials and division algebras, Annals of Mathematics59 (1954), 245–278.MathSciNetCrossRefGoogle Scholar
  24. 24.
    Generic splitting fields of central simple algebras, Annals of Mathematics62 (1955), 8–43.MathSciNetCrossRefGoogle Scholar
  25. 25.
    Identities and generators of matrix rings, Bulletin of the Research Council of Israel5A (1955), 5–10.MathSciNetGoogle Scholar
  26. 26.
    On rings with identities, Journal of the London Mathematical Society30 (1955), 464–470.zbMATHMathSciNetCrossRefGoogle Scholar
  27. 27.
    The T-ideals of the free rings, Journal of the London Mathematical Society30 (1955), 470–475.zbMATHMathSciNetCrossRefGoogle Scholar
  28. 28.
    The radical ring generated by a single element, Riveon lematematica9 (1955), 41–44 (in Hebrew; English summary).MathSciNetGoogle Scholar
  29. 29.
    Finite subgroups of division rings, Transaction of the American Mathematical Society80 (1955), 361–386.zbMATHMathSciNetCrossRefGoogle Scholar
  30. 30.
    Algebras over infinite fields, Proceedings of the American Mathematical Society7 (1956), 35–48.zbMATHMathSciNetCrossRefGoogle Scholar
  31. 31.
    Some results on central simple algebras, Annals of Mathematics63 (1956), 285–293.MathSciNetCrossRefGoogle Scholar
  32. 32.
    Radicals of polynomial rings, Canadian Journal of Mathematics8 (1956), 355–361.zbMATHMathSciNetGoogle Scholar
  33. 33.
    Invariant submodules of simple rings, Proceedings of the American Mathematical Society7 (1956), 987–989.MathSciNetCrossRefGoogle Scholar
  34. 34.
    Hermite rings and the equivalence of matrices, Riveon lematematica10 (1956), 41–45 (in Hebrew; English summary).MathSciNetGoogle Scholar
  35. 35.
    The scientific work of Prof. Jakob Levitzki, Riveon lematematica11 (1957), 1–6 (in Hebrew; English summary).MathSciNetGoogle Scholar
  36. 36.
    Derivations in simple rings, Proceedings of the London Mathematical Society7 (1957), 87–112.MathSciNetCrossRefGoogle Scholar
  37. 37.
    A generalization of Hilbert’s Nullstellensatz, Proceedings of the American Mathematical Society8 (1957), 649–656.zbMATHMathSciNetCrossRefGoogle Scholar
  38. 38.
    The radical of field extensions, Bulletin of the Research Council of Israel7F (1957/1958), 1–10.MathSciNetGoogle Scholar
  39. 39.
    Countably generated division algebras over non-denumerable fields, Bulletin of the Research Council of Israel7F (1957/1958), 39.Google Scholar
  40. 40.
    On arithmetic functions, Journal d’Analyse Mathematique5 (1956/1957), 273–314.MathSciNetCrossRefGoogle Scholar
  41. 41.
    Commutative linear differential operators, Pacific Journal of Mathematics8 (1958), 1–10.zbMATHMathSciNetGoogle Scholar
  42. 42.
    Rings with a pivotal monomial, Proceedings of the American Mathematical Society9 (1958), 635–642.zbMATHMathSciNetCrossRefGoogle Scholar
  43. 43.
    Simple algebras and cohomology groups of arbitrary fields, Transactions of the American Mathematical Society90 (1959), 73–112.zbMATHMathSciNetCrossRefGoogle Scholar
  44. 44.
    On the semi-simplicity of group algebras, Michigan Journal of Mathematics6 (1959), 251–253.zbMATHMathSciNetCrossRefGoogle Scholar
  45. 45.
    Some results on arithmetic functions, Journal of the Mathematical Society of Japan11 (1959), 275–290.MathSciNetGoogle Scholar
  46. 46.
    On the convolution of arithmetic functions, Riveon lematematica13 (1959), 1–12 (in Hebrew; English summary).MathSciNetGoogle Scholar
  47. 47.
    Finite dimensional central division algebras, Proceedings of the American Mathematical Society11 (1960), 28–31.zbMATHMathSciNetCrossRefGoogle Scholar
  48. 48.
    Arithmetic linear transformations and abstract prime number theorems, Canadian Journal of Mathematics13 (1961), 83–109.MathSciNetzbMATHGoogle Scholar
  49. 49.
    Groups with representations of bounded degree. II, Illinois Journal of Mathematics5 (1961), 198–205.zbMATHMathSciNetGoogle Scholar
  50. 50.
    Derived functors in abelian categories, Journal of Mathematical Mechanics10 (1961), 971–994.zbMATHMathSciNetGoogle Scholar
  51. 51.
    Homology groups and double complexes for arbitrary fields, Journal of the Mathematical Society of Japan14 (1962), 1–25.zbMATHMathSciNetCrossRefGoogle Scholar
  52. 52.
    On a lemma in elementary proofs of the prime number theorem, Bulletin of the Research Council of Israel10F (1962), 101–108.MathSciNetGoogle Scholar
  53. 53.
    Remarks on principal ideal rings, Osaka Mathematical Journal15 (1963), 59–69.zbMATHMathSciNetGoogle Scholar
  54. 54.
    Complexes of rings, Israel Journal of Mathematics2 (1964), 143–154.zbMATHMathSciNetCrossRefGoogle Scholar
  55. 55.
    Generalized polynomial identities and pivotal monomials, Transactions of the American Mathematical Society114 (1965), 210–226.zbMATHMathSciNetCrossRefGoogle Scholar
  56. 56.
    Identical relations in associative rings. Some Aspects of Ring Theory C.I.M.E. Conference II. Circolo (1965), pp. 1–48.Google Scholar
  57. 57.
    Jacobson-rings and Hilbert algebras with polynomial identities (co-author C. Procesi), Annali di Mathematica Pura et Applicata71 (1966), 61–72.zbMATHMathSciNetCrossRefGoogle Scholar
  58. 58.
    Nil semi-groups of rings with a polynomial identity, Nagoya Mathematical Journal27 (1966), 103–111.zbMATHMathSciNetGoogle Scholar
  59. 59.
    Rational identities and applications to algebra and geometry, Journal of Algebra3 (1966), 304–359.zbMATHMathSciNetCrossRefGoogle Scholar
  60. 60.
    Prime rings having polynomial identities with arbitrary coefficients, Proceedings of the London Mathematical Society17 (1967), 470–486.zbMATHMathSciNetCrossRefGoogle Scholar
  61. 61.
    Rings with involution, Israel Journal of Mathematics6 (1968), 99–106.zbMATHMathSciNetCrossRefGoogle Scholar
  62. 62.
    Correction to “Arithmetic linear transformations”, Canadian Journal of Mathematics21 (1969), 1–5.MathSciNetGoogle Scholar
  63. 63.
    Identities in rings with involutions, Israel Journal of Mathematics7 (1969), 63–68.zbMATHMathSciNetCrossRefGoogle Scholar
  64. 64.
    A noncommutative Hilbert basis theorem and subrings of matrices, Transactions of the American Mathematical Society149 (1970), 133–142.zbMATHMathSciNetCrossRefGoogle Scholar
  65. 65.
    Rings of quotients and Morita contexts, Journal of Algebra17 (1971), 273–298.zbMATHMathSciNetCrossRefGoogle Scholar
  66. 66.
    Embeddings in matrix rings, Pacific Journal of Mathematics36 (1971), 21–29.zbMATHMathSciNetGoogle Scholar
  67. 67.
    Some results on rings with polynomial identities, Actes du Congres International des Mathematiciens, Vol. 1 (Nice, 1970), Gauthier-Villars, Paris, 1970, pp. 269–272.Google Scholar
  68. 68.
    A note on PI-rings, Israel Journal of Mathematics10 (1971), 210–211.zbMATHMathSciNetCrossRefGoogle Scholar
  69. 69.
    Nil radicals. Historical notes and some new results, Colloq. Mathematical Society Janos Bolyai, Vol. 6:Rings, Modules and Radicals (Proc. Int. Colloq., Keszthely, Hungary), North-Holland, Amsterdam, 1971, pp. 47–65.Google Scholar
  70. 70.
    On rings of quotients, Symposia Mathematica8 (1972), 149–164.MathSciNetGoogle Scholar
  71. 71.
    On central division algebras, Israel Journal of Mathematics12 (1972), 408–420.zbMATHMathSciNetCrossRefGoogle Scholar
  72. 72.
    On univeral embeddings in matrix rings, Journal of the Mathematical Society of Japan25 (1973), 322–328.zbMATHMathSciNetGoogle Scholar
  73. 73.
    Polynomial identities and Azumaya algebras, Journal of Algebra27 (1973), 117–125.zbMATHMathSciNetCrossRefGoogle Scholar
  74. 74.
    On supernilpotent radicals, inEstudos de Matematica, Instituto de Alto Cultura, Lisbon, 1974, pp. 51–56.Google Scholar
  75. 75.
    Jacob Levitzki, 1904–1956, Israel Journal of Mathematics19 (1974), 1–2.MathSciNetCrossRefGoogle Scholar
  76. 76.
    The generic division rings, Israel Journal of Mathematics17 (1974), 241–247.zbMATHMathSciNetCrossRefGoogle Scholar
  77. 77.
    Polynomial identities, Israel Journal of Mathematics19 (1974), 183–199.MathSciNetCrossRefGoogle Scholar
  78. 78.
    Central embeddings in semi-simple rings, Pacific Journal of Mathematics56 (1975), 1–6.zbMATHMathSciNetGoogle Scholar
  79. 79.
    Identities and linear dependence, Israel Journal of Mathematics22 (1975), 127–137.zbMATHMathSciNetCrossRefGoogle Scholar
  80. 80.
    On a central identity for matrix rings, Journal of the London Mathematical Society14 (1976), 1–16.zbMATHMathSciNetCrossRefGoogle Scholar
  81. 81.
    Prime PI-rings (co-author L.W. Small), Bulletin of the American Mathematical Society83 (1977), 249–251.zbMATHMathSciNetGoogle Scholar
  82. 82.
    Alternating identities, inRing Theory (Proceedings of the Ohio University Conference on Ring Theory), Dekker, New York, 1978, pp. 1–14.Google Scholar
  83. 83.
    Generic abelian crossed products and p-algebras (co-author D. Saltman), Journal of Algebra51 (1978), 76–87.zbMATHMathSciNetCrossRefGoogle Scholar
  84. 84.
    Polynomials over division rings (co-author L.W. Small), Israel Journal of Mathematics31 (1978), 353–358.zbMATHMathSciNetCrossRefGoogle Scholar
  85. 85.
    The polynomial identities of associative rings. Noetherian rings and rings with polynomials identities. Proceedings of a conference, Durham, July (1978), pp. 1–38.Google Scholar
  86. 86.
    Division algebras of degree 4 and 8 with involution (co-authors L.H. Rowen and J.-P. Tignol), Bulletin of the American Mathematical Society1 (1979), 691–693.zbMATHMathSciNetGoogle Scholar
  87. 87.
    Division algebras of degree 4 and 8 with involution (co-authors L.H. Rowen and J.-P. Tignol), Israel Journal of Mathematics33 (1979), 133–148.zbMATHMathSciNetCrossRefGoogle Scholar
  88. 88.
    On the characteristic polynomial of a sum of matrices, Linear and Multilinear Algebra8 (1979/80), 177–182.MathSciNetCrossRefGoogle Scholar
  89. 89.
    Prime ideals in PI-rings (co-author L. W. Small), Journal of Algebra62 (1980), 358–383.zbMATHMathSciNetCrossRefGoogle Scholar
  90. 90.
    Generic splitting fields, inBrauer Groups in Ring Theory and Algebraic Geometry (Wilrijk, 1981), Lecture Notes in Mathematics917, Springer-Verlag, Berlin, 1982, pp. 1–24.CrossRefGoogle Scholar
  91. 91.
    Extension of derivations to central simple algebras, Communications in Algebra10 (1982), 797–803.zbMATHMathSciNetCrossRefGoogle Scholar
  92. 92.
    Division algebras. A survey, Contemporary Mathematics13 (1982), 3–26.zbMATHMathSciNetGoogle Scholar
  93. 93.
    PI-algebras and their cocharacters (co-author A. Regev), Journal of Algebra78 (1982), 248–254.zbMATHMathSciNetCrossRefGoogle Scholar
  94. 94.
    The sequence of codimensions of PI-algebras, Israel Journal of Mathematics47 (1984), 1–22.zbMATHMathSciNetCrossRefGoogle Scholar
  95. 95.
    Kummer subfields of Malcev-Neumann division algebras (co-author J.-P. Tignol), Israel Journal of Mathematics50 (1985), 114–144.zbMATHMathSciNetCrossRefGoogle Scholar
  96. 96.
    Symplectic modules (co-author J.-P. Tignol), Israel Journal of Mathematics54 (1986), 266–290.zbMATHMathSciNetCrossRefGoogle Scholar
  97. 97.
    Totally ramified splitting fields of central simple algebras over Henselian fields (co-author J.-P. Tignol), Institut Mathematique de l’Université Catholique de Louvain-La Neuve Vol.36 (1983), iv1-iv9; Journal of Algebra98 (1986), 95–101.Google Scholar
  98. 98.
    An example in central division rings, inPerspectives in Ring Theory (Antwerp, 1987), NATO Adv. Sci. Inst. Ser. C, Vol. 233, Kluwer, Dordrecht, 1988, pp. 85–92.Google Scholar
  99. 99.
    Finite-dimensional representations of PI algebras (co-author L.W. Small), Journal of Algebra133 (1990), 244–248.zbMATHMathSciNetCrossRefGoogle Scholar
  100. 100.
    GK-dimensions of corners and ideals (co-author L.W. Small), Israel Journal of Mathematics69 (1990), 152–160.zbMATHMathSciNetGoogle Scholar
  101. 101.
    Generic structures and division algebras, Seminaire Mathématique Rapport 171, Univ. Catholique de Louvain, 1990, pp. 1–12.Google Scholar
  102. 102.
    Galois splitting fields of a universal division algebra, Journal of Algebra143 (1991), 236–245.zbMATHMathSciNetCrossRefGoogle Scholar
  103. 103.
    Highlights in the history of finite-dimensional central division algebras, inRing Theory 1989, Israel Mathematics Conference Proceedings, Vol. 1, The Weizmann Science Press of Israel, Jerusalem, 1989, pp. 404–430.Google Scholar
  104. 104.
    Contributions of PI theory to Azumaya algebras, inRings, Extensions, and Cohomology, Lecture Notes in Pure and Applied Mathematics159, Dekker, New York, 1994, pp. 9–17.Google Scholar
  105. 105.
    Elements of reduced trace 0 (co-author L.H. Rowen), Israel Journal of Mathematics87 (1994), 161–179.zbMATHMathSciNetCrossRefGoogle Scholar
  106. 106.
    Affine algebras with polynomial identities (co-author L.W. Small), Rendiconti del Circolo Matematico di Palermo (2) Supplement31 (1993), 9–43.MathSciNetGoogle Scholar
  107. 107.
    Finite-dimensional representation of PI algebras. II (co-author L.W. Small), Journal of Algebra174 (1995), 848–855.zbMATHMathSciNetCrossRefGoogle Scholar
  108. 108.
    Recognition of matrix rings II (co-authors G. Agnarsson and J.C. Robson), Israel Journal of Mathematics96 (1996), 1–13 (this volume).zbMATHMathSciNetGoogle Scholar
  109. 109.
    Finite-dimensional subalgebras of division rings (co-author D. Baum), Israel Journal of Mathematics96 (1996), 15–22 (this volume).zbMATHMathSciNetGoogle Scholar
  110. 110.
    Algebras over infinite fields, revisited (co-author L.W. Small), Israel Journal of Mathematics96 (1996), 23–25 (this volume).zbMATHMathSciNetGoogle Scholar

Copyright information

© Hebrew University 1996

Authors and Affiliations

  • Avinoam Mann
    • 1
  1. 1.Institute of MathematicsThe Hebrew University of JerusalemJerusalemIsrael

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