Selected papers of S.A. Amitsur with commentary / Avinoam Mann ... [and others], editors.

Format:

Book

Author/Creator:

Amitsur, S. A. (Shimshon A.), 1921-1994.

Contributor:

Mann, Avinoam, 1937-2023.

Standardized Title:

Selections. English

Language:

English

Subjects (All):

Algebra.

Physical Description:

2 volumes : illustrations ; 26 cm

Place of Publication:

Providence, RI : American Mathematical Society, [2001]

Contents:

I. General Ring Theory

Commentary: Amitsur and Ring Theory / Louis H. Rowen 3

4. A generalization of a theorem on linear differential equations, Bull. Amer. Math. Soc. 54 (1948), 937-941 11

15. A general theory of radicals. I: Radicals in complete lattices, Amer. J. Math. 74 (1952), 774-786 17

20. A general theory of radicals: II. Radicals in rings and bicategories, Amer. J. Math. 75 (1954), 100-125 31

21. A general theory of radicals: III. Applications, Amer. J. Math. 75 (1954), 126-136 57

30. Algebras over infinite fields, Proc. Amer. Math. Soc. 7 (1956), 35-48 69

32. Radicals of polynomial rings, Canad. J. Math. 8 (1956), 355-361 83

33. Invariant submodules of simple rings, Proc. Amer. Math. Soc. 7 (1956), 987-989 91

35. Derivations in simple rings, Proc. London Math. Soc. 7 (1957), 87-112 95

37. The radical of field extensions, Bull. Research Council of Israel 7F (1957), 1-10 121

38. Countably generated division algebras over nondenumerable fields, Bull. Research Council of Israel 7F (1957), 39 131

40. Commutative linear differential operators, Pacific J. Math. 8 (1958), 1-10 133

41. Rings with a pivotal monomial, Proc. Amer. Math. Soc. 9 (1958), 635-642 143

43. On the semi-simplicity of group algebras, Michigan J. Math. 6 (1959), 251-253 151

49. Derived functors in abelian categories, Indiana J. Math. 10 (1961), 971-994 155

52. Remarks on principal ideal rings, Osaka Math. J. 15 (1963), 59-69 179

54. Generalized polynomial identities and pivotal monomials, Trans. Amer. Math. Soc. 114 (1965), 210-226 191

60. Rings with involutions, Israel J. Math. 6 (1968), 99-106 209

64. Rings of quotients and Morita contexts, J. Algebra 17 (1971), 273-298 217

68. Nil radicals. Historical notes and some new results, Coll. Math. Soc. Janos Bolyai 6. Rings, modules and radicals, Keszthely (Hungary) (1971), 47-65 243

69. On rings of quotients, Instituto Nazionale di Alta Mathematica, Symposia Mathematica VIII (1972), 149-164 263

102. Recognition of matrix rings II, (co-authors G. Agnarsson and J. C. Robson), Israel J. Math. 96 (1996), 1-13; part A 279

II. Rings Satisfying a Polynomial Identity

Commentary: Amitsur and PI-Rings / Lance W. Small 295

12. Nil PI-rings, Proc. Amer. Math. Soc. 3 (1951), 538-540 297

14. An embedding of PI-rings, Proc. Amer. Math. Soc. 3 (1952), 3-9 301

26. On rings with identities, J. London Math. Soc. 30 (1955), 464-470 309

27. The T-ideals of the free ring, J. London Math. Soc. 30 (1955), 470-475 317

36. A generalization of Hilbert's Nullstellensatz, Proc. Amer. Math. Soc. 8 (1957), 649-656 323

48. Groups with representations of bounded degree II, Illinois J. Math. 5 (1961), 198-205 331

56. Jacobson-rings and Hilbert algebras with polynomial identities, (coauthor C. Procesi), Annali di Mathematica Pura et Applicata 71 (1966), 61-72 339

57. Nil semi-groups of rings with a polynomial identity, Nagoya Math. J. 27 (1966), 103-111 351

58. Rational identities and applications to algebra and geometry, J. Algebra 3 (1966), 304-359 361

59. Prime rings having polynomial identities with arbitrary coefficients, Proc. London Math. Soc. 17 (1967), 470-486 417

62. Identities in rings with involutions, Israel J. Math. 7 (1969), 63-68 435

63. A noncommutative Hilbert basis theorem and subrings of matrices, Trans. Amer. Math. Soc. 149 (1970), 133-142 441

65. Embeddings in matrix rings, Pacific J. Math. 36 (1971), 21-29 451

66. Some results on rings with polynomial identities, Proc. International Congress of Math. I (1970), 269-272 461

67. A note on PI-rings, Israel J. Math. 10 (1971), 210-211 465

71. On universal embeddings in matrix rings, J. Math. Soc. of Japan 25 (1973), 322-328 467

72. Polynomial identities and Azumaya algebras, J. Algebra 27 (1973), 117-125 475

75. Polynomial identities, Israel J. Math. 19 (1974), 183-199 485

76. Central embeddings in semi-simple rings, Pacific J. Math. 56 (1975), 1-6 503

81. Polynomials over division rings, (co-author L. W. Small), Israel J. Math. 31 (1978), 353-358 509

85. Prime ideals in PI-rings, (co-author L. W. Small), J. Algebra 62 (1980), 358-383 515

95. Finite-dimensional representations of PI-algebras, (co-author L. W. Small), J. Algebra 133 (1990), 244-248 541

96. GK-dimensions of corners and ideals, (co-author L. W. Small), Israel J. Math. 69 (1990), 152-160 547

99. Contributions of PI theory to Azumaya algebras, (1994), 9-17; Rings extensions and cohomology (Evanston, IL 1993), Lecture Notes in Pure and Applied Math., vol. 159, Dekker 557

101. Finite dimensional representation of PI algebras II, (co-author L. W. Small), J. Algebra 174 (1995), 848-855 567

104. Algebras over infinite fields, revisited, (co-author L. W. Small), Israel J. Math. 96 (1996), 23-25; part A 575

III. Combinatorial Polynomial Identity Theory

Commentary: Amitsur and Combinatorial P.I. Theory / Amitai Regev 3

9. Minimal identities for algebras, (co-author J. Levitzki), Proc. Amer. Math. Soc. 2 (1950), 449-463 7

11. Remarks on minimal identities for algebras, (co-author J. Levitzki), Proc. Amer. Math. Soc. 2 (1951), 320-327 23

17. The identities of PI-rings, Proc. Amer. Math. Soc. 3 (1952), 27-34 31

25. Identities and generators of matrix rings, Bull. Research Council of Israel 5A (1955), 1-10 39

77. Identities and linear dependence, Israel J. Math. 22 (1975), 127-137 45

78. On a central identity for matrix rings, J. London Math. Soc. 14 (1976), 1-6 57

79. Alternating identities, Proc. Ohio Univ. Conference on Ring Theory. Dekker (1978), 1-14 63

89. PI-algebras and their cocharacters, (co-author A. Regev), J. Algebra 78 (1982), 248-254 77

90. The sequence of co-dimensions of PI-algebras, Israel J. Math. 47 (1984), 1-22 85

IV. Division Algebras

Commentary: Amitsur and Division Algebras / David J. Saltman 109

5. Contributions to the theory of central simple algebras, Summary of thesis submitted to the Hebrew University, 1949, pp. 1-28 117

7. La representation d'algebres centrales simples, Comp. rendus des seance de l'Acad. des Science t.230 (1950), 902-904 137

8. Construction d'algebres centrales simples sur des corps de characteristique zero, Comp. rendus des seance de l'Acad. des Science t.230 (1950), 1026-1028 141

22. Non-commutative cyclic fields, Duke Math. J. 21 (1954), 87-105 145

23. Differential polynomials and division algebras, Ann. of Math. 59 (1954), 245-278 165

24. Generic splitting fields of central simple algebras, Ann. of Math. 62 (1955), 8-43 199

29. Finite subgroups of division rings, Trans. Amer. Math. Soc. 80 (1955), 361-386 235

31. Some results on central simple algebras, Ann. of Math. 63 (1956), 285-293 261

39. On arithmetic functions, J. Analyse de Math. 5 (1958), 273-314 271

42. Simple algebras and cohomology groups of arbitrary fields, Trans. Amer. Math. Soc. 10 (1959), 73-112 313

44. Some results on arithmetic functions, J. Math. Soc. of Japan 11 (1959), 275-290 353

46. Finite dimensional central division algebras, Proc. Amer. Math. Soc. 11 (1960), 28-31 369

50. Homology groups and double complexes for arbitrary fields, J. Math. Soc. of Japan 14 (1962), 1-25 373

51. On a lemma in elementary proofs of the prime number theorem, Bull. Research Council of Israel 10F (1962), 101-108 399

53. Complexes of rings, Israel J. Math. 2 (1964), 143-154 407

70. On central division algebras, Israel J. Math. 12 (1972), 408-420 419

74. The generic division rings, Israel J. Math. 17 (1974), 241-247 433

80. Generic abelian crossed products and p-algebras, (co-author D. Saltman), J. Algebra 51 (1978), 76-87 441

83. Division algebras of degree 4 and 8 with involution, (co-authors L. H. Rowen, J. P. Tignol), Bull. Amer. Math. Soc. 1 (1979), 691-693; Israel J. Math. 33 (1979), 133-148 453

84. On the characteristic polynomial of a sum of matrices, Linear and Multilinear Algebra 8 (1980), 177-182 469

86. Generic splitting fields. Brauer groups in ring theory and algebraic geometry, Proc. Antwerp (1981), 1-23; Lecture Notes in Math. 917, Springer-Verlag 475

87. Extension of derivations to central simple algebras, Comm. Algebra 10 (1982), 797-803 499

91.

Kummer subfields of Malcev-Neumann division algebra, (co-author J. P. nignol), Israel J. Math. 50 (1985), 114-144 507

92. Symplectic modules, (co-author J. P. Tignol), Israel J. Math. 54 (1986), 266-290 539

93. Totally ramified splitting fields of central simple algebras over Henselian fields, (co-author J. P. Tignol), J. Algebra 98 (1986), 95-101 565

97. Galois splitting fields of a universal division algebra, J. Algebra 143 (1991), 236-245 573

100. Elements of reduced trace 0, (co-author L. H. Rowen), Israel J. Math. 87 (1994), 161-179 583

103. Finite-dimensional subalgebras of division rings, (co-author D. Baum), Israel J. Math. 96 (1996), 15-22; part A 603.

Notes:

Includes bibliographical references.

ISBN:

0821806882

0821829246

0821829254

OCLC:

47140704