PUBLICATIONS

Research Announcements, General, etc

1. La noción de ]'Angulo y el Sentido en el Plano, Conceptos de Matemática, vols. 9 e 10, Buenos Aires, 1968.

2. The Nilpotency of the Group of Units of a Group Ring, Atas da III Escola de Álgebra, SBM, Rio de Janeiro, 1974, pp.151 - 162.

3. The Group of Units of ${\bf Z}D_4$, Atas da III Escola de Álgebra, SBM, Rio de Janeiro, 1974, pp. 163 - 170.

4. A Gênese da Álgebra Moderna, Suplemento Cultural de O Estado de São Paulo, ano I , $N^o$ 17.

5. A História da Álgebra Abstrata, Suplemento Cultural de O Estado de São Paulo, ano I , $N^o$ 18.

6. Certain Properties of the Group of Units of a Group Ring, Atas do XI Colóquio Brasileiro de Matemática

7. Gauss, o Príncipe da Matemática, Suplemento Cultural de O Estado de São Paulo, ano II, $N^o$ 83, (1978), pp. 14 - 15.

8. Torsion Units in Group Rings, Atas do XII Colóquio Brasileiro de Matemática

9. On Group Rings with t.p.p., Atas da VI Escola de Álgebra, SBM, Rio de Janeiro,

10. On a Conjecture of Zassenhaus, Atas da VII Escola de Álgebra, SBM, Rio de Janeiro,

11. On a Conjecture of H. J. Zassenhaus on Torsion Units of Finite Order in Integral Group Rings, Atas da VIII Escola de Álgebra, Vol I, SBM, Rio de Janeiro, 1985, pp. 125 - 131.

12. Isomorphisms and Units in Alternative Group Rings, Atas da IX Escola de Álgebra, Vol I, SBM, Brasília, 1986, pp. 183 - 188.

13. História da Álgebra Abstrata, Coleç ao Tópicos da Matemática Elementar, IMEUSP, São Paulo, 1987, pp. 38 - 61.

14. Classes de Conjugação Finitas em Anéis de Grupo, Atas da X Escola de Álgebra, Vol I, SBM, Rio de Janeiro, 1990, pp. 59 -68 (with Sônia P. Coelho).

15. Groups whose Quotients by their Centers are Isomorphic to $C_p \times C_p$, Atas da XI Escola de Álgebra, Vol I, SBM, São Paulo, 1990, pp. 93 - 97(with Guilherme Leal).

16. Derivations of Full Matrix Rings, Atas da XI Escola de Álgebra, Vol I, SBM, São Paulo, 1990, pp. 99 - 103 (with Sônia P. Coelho).

17. A Emergência dos Números Complexos, Revista do Prof. de Mat., 24, (1993), 5 - 15.

18. Indecomposable RA loops and the Isomorphism Problem, I Encontro de Álgebra IMEUSP-IMECCUNICAMP, RT. MAT. 93-15 (1993), 10-15.

19. Group Algebras of Dihedral Groups, II Encontro de Álgebra IMEUSP-IMECCUNICAMP, Campinas, 1994, pp. 15-20.

20. A Solução de Tartaglia para a Equação de Terceiro Grau, Revista do Prof. de Mat., 25. (1994), 16-22.

21. Units in Alternative Loop Rings and the Conjectures of H.J. Zassenhaus, Atas da XIII Escola de Álgebra, IMECC-UNICAMP, Campinas, 1995, pp. 193-200.

22. Álgebras alternativas com propriedade de torção, atas do VI Encontro em Álgebra, realizado na Unicamp, São Paulo, 1997, pp. 77-82.

23. The Torsion Product Property in Alternative Algebras, Proc. of the International Congress in Algebra and Combinatorics 1997, Springer-Verlag, to appear.

Published Papers

1. The Nilpotency of the Group of Units of a Group Ring, Atas da III Escola de Álgebra, Soc. Brasileira de Mat.,Rio de Janeiro, 1974, pp. 151 - 162.

2. The Group of Units of the Integral Group Ring $ZD_{4}$, Bol. Soc. Brasileira de Mat., 4, 2, (1973) 85 - 92.

3. Integral Group Rings with Nilpotent Unit Groups, Canad. J. of Math., 28, 5, (1976) 954 - 960.

4. Group Rings whose Units form a Nilpotent or FC Group, Proc. Amer. Math. Soc., 68, 2, (1978) 247 - 248 (with M.M. Parmenter).

5. p-adic Group Rings with Nilpotent Unit Groups, J. of Pure and Appl. Algebra, 12, (1978) 147 - 151.

6. Isomorphic Group Rings of Direct Products, Archiv der Math., 31, (1978) 11 - 14 (with M.M. Parmenter).

7. Group Rings whose Units form an FC group, Archiv der Math., 30 (1978) 380 - 384.

8. On the Isomorphism Problem for Group Rings of Finite Groups, Atas da IV Escola de Álgebra, Soc. Bras. de Mat. , Rio de Janeiro, 1979, pp. 81 - 95.

9. Group Rings over $Z_{(p)}$ with FC Unit Groups, Canad. J. of Math. , 32, 5 (1980), 1268 - 1269 (with H. Merklen).

10. Group Rings whose Torsion Units form a Subgroup, Proc. Amer. Math. Soc., 81, 2, (1981) 172 - 174.

11. Group Rings whose Torsion Units form a Subgroup II, Comm. in Algebra, 9, 7, (1981) 699 - 712.

12. FC elements in Group Rings, Comm. in Algebra, 9, 12, (1981) 1285 - 1293 (with S.K. Sehgal).

13. A note on Isomorphic Group Rings, Bol. Soc. Brasileira de Mat., 12, 2, (1981) 57 - 59 (with M.M. Parmenter).

14. Units in Group Rings: a short survey, in Groups St. Andrews - 1981 , ed by C. M. Campbell and E. F. Robertson, London Math. Soc. Lecture Notes Series $N^o 71$, Cambridge Univ. Press, London 1982, pp. 281 - 297.

15. The Early History of Group Rings, in Groups St. Andrews - 1981, ed. by C. M. Campbell and E. F. Robertson, London Math. Soc. Lecture Notes Series, $N^o 71$, Cambridge Univ. Press, London 1982, pp. 270 - 280.

16. O Problema do Isomorfismo para Anéis de Grupo, Not. Soc, Brasileira de Mat. , 13, 1, (1982) 5 -21.

17. Torsion Units of Integral Group Rings of Metacyclic Groups, J. of Number Theory, 19, 1, (1984) 103 - 114 (with S.K. Sehgal).

18. Torsion Units in Group Rings and a Conjecture of H. J. Zassenhaus, in Group and Semigroup Rings, ed. by G. Karpilovsky, North Holland Math. Studies $N^o 126$, Amsterdam, 1985, pp. 179 - 192.

19. Derivations with Invertible Values in Rings with Involutions, Pacific J. of Math., 123, 1, (1986) 47 - 54 (with A Giambruno and P. Misso).

20. A Conjecture of Zassenhaus on Torsion Units of Integral Group Rings II, Proc. Amer. Math. Soc., 97, 3, (1986) 201 - 206 (with J. Ritter and S.K. Sehgal).

21. Isomorphisms and Units in Alternative Loop Rings, Comptes Rendus of the Canad. Acad. of Sciences, 9, (1987) 259 - 263 (with E.G. Goodaire).

22. A note on Central Idempotents in Group Rings II, Proc. Edinburgh Math. Soc., 31, (1988) 211 - 215 (with S.P. Coelho).

23. Isomorphisms of Integral Alternative Loop Rings, Rend. Circolo Mat. Palermo, 2, 37, (1988) 126 - 135 (with E.G. Goodaire).

24. Anéis de Loop Alternativos, Atas do XVI Colóquio Brasileiro de Mat., IMPA, Rio de Janeiro, 1988, pp. 16 - 32 (with E.G. Goodaire).

25. Torsion Units in Alternative Loop Rings, Proc. Amer. Math. Soc., 107, 1, (1989) 7 - 15 (with E.G. goodaire).

26. Supercenters and FC Units in Group Rings, Israel Math. C. Proc., 1, (1989) 74 - 78 (with S.P. Coelho).

27. Finite Conjugacy in Group Rings, Comm. in Algebra, 19, 3, (1991) 981 - 995 (with S.P. Coelho).

28. Indecomposable R.A. Loops and their Loop Algebras , Comptes Rendus of the Canad. Acad. of Sciences, 25,5 (1992), 189 - 194 (with E. Jespers and G. Leal).

29. Isomorphic Group (and Loop) Algebras, J. of Algebra, 155 (1993), 195 - 210 (with G. Leal).

30. Derivations of Upper Triangular Matrix Rings, Linear Algebra and its Appl., 187 (1993), 263 - 237 (with S.P. Coelho).

31. Group Rings whose Torsion Units form a Subgroup, Proc. Edinburgh Math. Soc, 37, (1994), 201-205 (with S.P. Coelho).

32. Loop Algebras of Indecomposable R.A Loops, Comm. in Algebra, 22, 4 (1994), 1369-1379 (with E. Jespers and G. Leal).

33. Units of Integral Group Rings of some Metacyclic Groups . Can. Math. Bull., 37, 2(1994), 223-237 (with E. Jespers and G. Leal).

34. Indecomposable R.A. Loops and related topics, Mat. Contemp, 6 (1994), 137-145.

35. On a Conjecture of Zassenhaus in an Alternative Setting. Comptes Rendus of the Canad. Acad. of Sciences, 16, 2-3(1994), 75-78 (with E.G. Goodaire).

36. Ring Alternative Loops and their Loop Rings, Resenhas Inst. Mat. Est. Univ. São Paulo, 2, 1(1995), 47-82 (with E.G. Goodaire).

37. Modular Loop Algebras of R.A. Loops, J. of Algebra, 175 (1995), 1027-1040 (with L.G.X. de Barros).

38. Classifying Indecomposable R.A. Loops, J. of Algebra, 176 (1995), 569-584 (with E. Jespers and G. Leal).

39. On the Loop of Units of an Alternative Loop Ring, Nova J. of Algebra and Geometry, 3,3 (1995), 199-208 (with E.G. Goodaire).

40. A Note on Derivations of Group Rings, Canad. Math. Bull., 38, 4 (1995), 434-437 (with A. Giambruno e M. Ferrero).

41. Loop Algebras of Code Loops, Comm. in Algebra, 23, 13 (1995), 4781-4790 (with L.G.X. de Barros).

42. Finite conjugacy and nilpotency in loops of units, C.R. Math. Rep. Acad. Sci. Canada, 17 (1995),201-206 (with E.G. Goodaire).

43. Automorphisms of Group Algebras of Dihedral Groups, Boll. Unione Mat. Italiana, 3, 9 (1995), 541-548 (with Sônia P. Coelho).

44. Units of Group Rings, J. of Pure and Appl. Algebra, 107 (1996), 233-251 (with E. Jespers).

45. The torsion product property in alternative algebras, J. of Algebra, 184 (1996), 58-70 (with E. G. Goodaire).

46. Finite Subloops of Units in an Alternative Loop Ring, Proc. Amer. Math. Soc., 124, 4 (1996), 995-1002 (with E.G. Goodaire).

47. Finite Conjugacy in Alternative Loop Rings, Comm. in Algebra, 24, 3 (1996), 881-889 (with E. G. Goodaire).

48. Automorphisms of Group Algebras of some Metacyclic Groups,Commun. Algebra, 24, 13 (1996), 4135-4145 (with S. P. Coelho e Eric Jespers).

49. Central idempotents in alternative loop rings, Nova J. of Math., Game Theory and Algebra, 5, 3 (1996), 207-214 (with E. G. Goodaire).

50. On the Loop of Units of an Alternative Loop Ring. Comptes Rendus of the Canad. Acad. of Sciences, 5, 3 (1996), 207-214 (with E. G. Goodaire).

51. Nilpotent Moufang Loops of Units, J. of Algebra, 190 (1997), 88-99 (with E.G. Goodaire).

52. Integral Group Rings of Frobenius Groups and the Conjectures of H.J. Zassenhaus, Comm. in Algebra, 25, 7 (1997), 3211-3225 (with S.O. Juriaans e M. Dokuchaev).

53. Some Remarks on central idempotents in group rings, Publ. Math. (Debrecen), 52, 1-2 (1998), 187-192 (with S.P. Coelho).

54. Torsion Subgroups of Units in Artinian Rings, in ``Methods in Ring Theory'', ed. by V. Drensky, A. Giambruno and S.K. Sehgal, Marcel Dekker, New York, 1998, pp. 75-81 (with S.P. Coelho).

55. Nilpotent elements and ideals in alternative loop rings, East-West J. of Math, 2 (1999), 159-169 (com A. Zatelli) (submitted by invitation of the editors).

56. The Torsion Product Property in Alternative Algebras II, Comm. in Algebra, 27, 6 (1999), 2905-2911.

57. Some results on Integral Group Rings of Frobenius Groups, Mat. Contemporánea, 16 (1999), 227-236.

58. Alternative loop rings and related topics, in Algebra: recent advances, ed. by I.B.S. Passi, Indian Math. Society, Hindustan book agency, New Dehli, 1999, pp. 117-133 (submitted by invitation of the editor).

59. Central Units of Integral Group Rings, Commun. in Algebra, 27, 12 (1999), 6233-6241 (with S.K. Sehgal).

60. The torsion product property in Alternative Algebras, in Algebras and Combinatorics, ed. by K.P. Shum, E.J. Taft and Z.X. Wan, Springer-Verlag, Singapore, 1999, pp. 353-358.

61. More on the units of an alternative loop ring, C.R. Math. Rep. Acad. Sci. Canada,1 (2000), 28-32 (with E.G. Goodaire).

62. FC centres of units in algebras and orders, C.R. Math. Rep. Acad. Sci. Canada, 1 (2000), 25-27 (with M. Dokuchaev, S.O. Juriaans and M.L.S. Singer).

63. Units of Integral Group Rings of Frobenius Groups, J. of Group Theory, 3 (2000), 277-284 (with S.O. Juriaans).

64. Normal Subloops in the Integral Loop Ring of an RA Loop, Can. Math. Bull., 44, 1 (2001), 27-35 (with E.G. Goodaire).

65. Finite conjugacy in algebras and orders, Proc. Edinburgh Math. Soc., 44 (2001), 201-213 (with M. Dokuchaev, S.O. Juriaans and M.L.S. Singer).

66. Alternative loop rings with solvable unit loops, J. of Algebra, 240 (2001), 25-39. (with E.G. Goodaire).

67. Normal subgroups of the group of units in the group rings of torsion groups, Publ. Math. (Debrecen), 59, 1-2 (2001), 235-242 (with A.A. Bovdi).

68. FC elements in algebras and orders, Mat. Contemporánea, to appear.

69. A normal complement for an RA loop in its integral loop ring, Quaestiones Mathematicae, to appear (with E.G. Goodaire).

70. The normalizer propery for integral group rings of Frobenius groups, J. of Algebra, to appear (with T. Petit Lobão).

Papers Submitted.

1. The smallest simple Moufang Loop (with M.L. Merlini Giuliani).

2. Units in Group Rings of Torsion Groups (with A.A. Bovdi).

Books

1. Anéis e Módulos, Publicações do IME- USP, São Paulo, 1973.

2. Anéis de Grupo, IV Escola de Álgebra, São Paulo, 1976.

3. História da Geomeria Clássica, FTD, São Paulo, to appear (with J.H. Bussab).

4. Alternative Loop Rings, North Holland Math. Studies N. 184, Elsevier, Amsterdam, 1996 (with E.G. Goodaire e E. Jespers).

5. Unidades de Anéis de Grupo, Monografias de Matemática 58, IMPA, Rio de Janeiro, 1998.

6. Números: Uma Introdução à Matemática, EDUSP, São Paulo, 1998 (with Sônia P. Coelho).

7. An Introduction to Group Rings, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2002, 371 pp. (with S.K. Sehgal).

Chapters of Books

1. Ideais em Anéis de Grupo, in Atas da VIII Escola de Álgebra, Soc. Brasileira de Mat., Rio de Janeiro, 1985, pp. 75 - 127 (with S.P. Coelho).

2. Breve Introdução à História da Teoria de Anéis, in Atas da XI Escola de Álgebra, Soc. Brasileira de Mat., São Paulo, 1990, pp. 1 - 46.

3. Breve Introdução à História da Teoria de Grupos, in Atas da XII Escola de Álgebra, Soc. Brasileira de Mat., to appear.

4. Contar, calcular, compreender: a aritmética na Idade Média, in Trivium e Quadrivium, org. by Lênia Márcia Mogelli, Ibis, Cotia, SP, 1999, pp. 161-202.