Publications

Articles

1) A. Giambruno, Algebraic conditions on rings with involution, J. Algebra, 50 (1978), 190-212.

2) A. Giambruno, Periodic n-th commutators of traces in rings with involution, Rend. Circ. Mat. Palermo (2), 27 (1978), 61-72.

3) A. Giambruno, Some generalizations of the center of a ring, Rend. Circ. Mat. Palermo (2), 27 (1978), 270-282.

4) A. Giambruno, Un teorema su anelli con involuzione, Boll. Un. Mat. It. (5), 16-A (1979), 625-629.

5) B. Felzenszwalb and A. Giambruno, Centralizers and multilinear polynomials in non-commutative rings, J. London Math. Soc. (2), 19 (1979), 417-428.

6) A. Giambruno, Rings f-radical over PI-subrings, Rend. Mat. (4), 13} (1980), 105-113.

7) B. Felzenszwalb and A. Giambruno, Periodic and nil polynomials in rings, Canad. Math. Bull. (4), 23 (1980), 473-476.

8) A. Giambruno, On derivations in prime rings, Atti Convegno "Codages et Transduction", Firenze (1980), 200-207.

9) A. Giambruno and I. N. Herstein, Derivations with nilpotent values, Rend. Circ. Mat. Palermo (2), 30 (1981), 199-206.

10) B. Felzenszwalb and A. Giambruno, A commutativity theorem for rings with derivations, Pacific J. Math., 102 (1982), 41-45.

11) A. Giambruno, On the symmetric hypercenter of a ring, Canad. J. Math., 34 (1984), 421-435.

12) B. Felzenszwalb and A. Giambruno, F-algebraic extensions of rings, Arch. Math., 43 (1984), 124-131.

13) L. Carini and A. Giambruno, Lie ideals and nil derivations, Boll. Un. Mat. It. (6), 4-A (1985), 497-503.

14) A. Giambruno and A. Regev, Wreath products and PI-algebras, J. Pure Applied Algebra, 35 (1985), 133-149.

15) A. Giambruno, P. Misso and C. Polcino Miles, Derivations with invertible values in rings with involution, Pacific J. Math., 123 (1986), 47-54.

16) A. Giambruno, GL x GL - representations and *-polynomial identities, Comm. Algebra, 14 (1986), 787-796.

17) A. Giambruno, Rappresentazioni di gruppi simmetrici ed identità polinomiali, Rend. Sem. Mat. Univ. Milano, 56 (1986), 13-22.

18) A. Giambruno and J. Bergen, f-radical extensions of rings, Rend. Sem. Mat. Univ. Padova, 77 (1987), 125-133.

19) A. Giambruno, Polynomial identities with involution and the hyperoctahedral group, Group Theory, O. H. Kegel, F. Menegazzo and G. Zacher eds., Springer-Verlag, 1987, 18-25.

20) O. M. Di Vincenzo and A. Giambruno, Modular representation theory and PI-algebras, Comm. Algebra, 16 (1988), 2043-2067.

21) A. Giambruno and S. K. Sehgal, A Lie property in group rings, Proc. Amer. Math. Soc., 105 (1989), 287-292.

22) A. Giambruno and A. Valenti, Nil *-polynomials in rings, Linear and Multilinear Algebra, 24 (1989), 127-134.

23) A. Giambruno and S. K. Sehgal, On a polynomial identity for n x n matrices, J. Algebra, 126 (1989), 451-453.

24) A. Giambruno, S. K. Sehgal and A. Valenti, Automorphisms of the integral group ring of the hyperoctahedral group, Comm. Algebra, 18 (1990), 1989-2005.

25) A. Giambruno, On *-polynomial identities for n x n matrices, J. Algebra, 133 (1990), 433-438.

26) A. Giambruno, S. K. Sehgal and A. Valenti, Automorphisms of the integral group ring of some wreath products, Comm. Algebra, 19 (1991), 519-534.

27) A. Giambruno and S. K. Sehgal, Automorphisms of the integral group ring of the wreath product of a p-group with S_n, Rocky Mountain J. Math., 22 (1992), 1303-1316.

28) A. Giambruno and S. K. Sehgal, Lie nilpotence of group rings, Comm. Algebra, 21 (1993), 4253-4261.

29) Y. Bahturin and A. Giambruno, Identities of sums of commutative subalgebras, Rend. Circ. Mat. Palermo, 43 (1994), 250-258.

30) A. Giambruno, J. Z. Goncalves and A. Mandel, Rings with algebraic n-Engel elements, Comm. Algebra, 22 (1994), 1685-1701.

31) V. Drensky and A. Giambruno, Cocharacters, codimensions and Hilbert series of the polynomial identities for 2 x 2 matrices with involution, Canad. J. Math., 46 (1994), 718-733.

32) A. Giambruno, E. Jespers and A. Valenti, Group identities on units of rings, Arch. Math., 63 (1994), 291-296.

33) A. Giambruno, and S. K. Sehgal, Generators of large subgroups of units of integral group rings of nilpotent groups, J. Algebra, 174 (1995), 150-156.

34) V. Drensky and A. Giambruno, On the *-polynomial identities of minimal degree for matrices with involution, Boll. Un. Mat. It. (7), 9-A (1995), 471-482.

35) M. Ferrero, A. Giambruno and C. Polcino Milies, A note on derivations of group rings, Canad. Math. Bull., 38 (1995), 434-437.

36) A. Giambruno and A. Valenti, On minimal *-identities of n x n matrices, Linear and Multilinear Algebra, 39 (1995), 309-323.

37) A. Berele, A. Giambruno and A. Regev, Involution codimensions and trace codimensions of matrices are asymptotically equal, Israel J. Math. 96 (1996), 49-62.

38) A. Giambruno, Units of group rings and their group identities, Resenhas IME-USP, 2 (1996), 275-282.

39) A. Giambruno and A. Valenti, Central polynomials and matrix invariants, Israel J. Math. 96 (1996), 281-297.

40) A. Giambruno, Identità polinomiali per matrici oblique o simmetriche, Atti Acad. Sci. Lett. Arti Palermo, (5) 17, (1996-97), 109-116.

41) A. Giambruno, Polinomi centrali ed invarianti matriciali, Atti Acad. Sci. Lett. Arti Palermo, (5) 17, (1996-97), 117-126.

42) A. Giambruno, S. K. Sehgal and A. Valenti, Group algebras whose units satisfy a group identity, Proc. Amer. Math. Soc. 125 (1997), 629-634.

43) A. Giambruno, On permutations of class sums of alternating groups, Comm. Algebra} 25 (1997), 2327-2331.

44) Y. Bahturin, - A. Giambruno and M. Zaicev, Symmetric identities in graded algebras, Arch. Math. 69 (1997), 461-464.

45) A. Giambruno, Y. Bahturin and D. Riley, Group-graded algebras satisfying apolynomial identity, Israel J. Math. 148 (1998), 145-155.

46) A. Giambruno and M. Zaicev, PI-Algebras and Codimension Growth, Methods in Ring Theory, V. Drensky, A. Giambruno and S. K. Sehgal eds., Marcel Dekker, New York, 1998, 115-120.

47) A. Giambruno, S. K. Sehgal and A. Valenti, Symmetric Units and Group Identities, Manuscripta Mathematica 96 (1998), 443-461.

48) A. Giambruno and M. Zaicev, On codimension growth of finitely generated associative algebras, Adv. Math. 146 (1998), 145-155.

49) A. Giambruno and E. Jespers, Central idempotents and units in rational group algebras of alternating groups, Int. J. Algebra Comp. 8 (1998), 467-477.

50) Y. Bahturin, A. Giambruno and M. Zaicev, G-identities on associative algebras, Proc. Amer. Math. Soc. 127 (1999), 63-69.

51) A. Giambruno and M. Zaicev, Exponential codimension growth of PI-algebras: an exact estimate, Adv. Math. 142 (1999), 221-243.

52) A. Giambruno, A. Regev and M. Zaicev, On codimension growth of finite dimensional Lie algebras, J. Algebra 220 (1999), 466-474.

53) A. Giambruno and M. Zaicev, Involution codimensions of finite dimensional algebras and exponential growth, J. Algebra 222 (1999), 471-484.

54) A. Giambruno, S. Mishchenko and M. Zaicev, On the colength of a variety of Lie algebras, Internat J. Algebra Comput. 9 (1999), 483-491.

55) A. Y. Bahturin, A. Giambruno and M. Zaicev, Codimension growth and graded identities, in "Algebra", De Gruyter, Berlin, 57-76, 2000.

56) A. Giambruno, S. K. Sehgal and A. Valenti, Group identities on units of group algebras, J. Algebra 226 (2000), 488-504.

57) A. Giambruno and M. Zaicev, A characterization of varieties of associative algebras of exponent two, Serdica Math. J. 26 (2000), 245-252.

58) A. Giambruno and M. Zaicev, Minimal varieties of algebras of exponential growth, Electron. Res. Announc. Amer. Math. Soc. 6 (2000), 40-44.

59) A. Giambruno, A. Regev and M. Zaicev, Simple and semisimple Lie algebras and codimension growth, Trans. Amer. Math. Soc. 352 (2000), 1935-1946.

60) A. Giambruno and M. Zaicev, A characterization of algebras with polynomial growth of the codimensions, Proc. Amer. Math. Soc. 129 (2001), 59-67.

61) A. Giambruno and S. Mishchenko, Polynomial growth of the *-codimensions and Young diagrams, Comm. Algebra 29 (2001), 277-284.

62) A. Giambruno and S. Mishchenko, On star-varieties with almost polynomial growth, Algebra Colloquium 8 (2001), 33-42.

63) A. Giambruno, A combinatorial approach to the theory of PI-algebras and exponential growth, Algebraic combinatorics and computer science, 493-511, Springer Italia, Milan, 2001.

64) A. Giambruno and P. Koshlukov, On the identities of the Grassmann algebras in characteristic p>0, Israel J. Math. 122 (2001), 305-316.

65) A. Giambruno and S. Mishchenko and M. Zaicev, Polynomial identities on superalgebras and almost polynomial growth, Comm. Algebra, 29 (2001), 3787-3800.

66) A. Giambruno and S. Mishchenko and M. Zaicev, Group actions and asymptotic behaviour of graded polynomial identities, J. London Math. Soc. (2) 66 (2002), 295-312.

67) A. Giambruno and M. Zaicev, Asymptotics for the standard and the Capelli identities, (Russian) Uspekhi Mat. Nauk. 57 (2002), 179-180; translation in: Russian Math. Surveys 57 (6) (2002), 1222-1223.

68) A. Giambruno and C. Polcino Milies, Lie nilpotence in group rings, Resenhas IME-USP, vol 5 No. 4, (2002), 363-370.

69) A. Giambruno and M. Zaicev, Minimal varieties of algebras of exponential growth, Adv. Math.174 (2003), 310-323.

70) B. Felzenszwalb, A. Giambruno and G. Leal, On rings which are sums of two PI-subrings: a combinatorial approach, Pacific J. Math. 209 (2003), 17-30.

71) A. Giambruno and M. Zaicev, Asymptotics for the standard and the Capelli identities, Israel J. Math. 135 (2003), 125-145.

72) A. Giambruno and M. Zaicev, Minimal manifolds with a given growth of codimensions, (Russian) Vestnik Moskov. Univ. Ser. I Mat. Mekh. 71 (2003), 20-22; translation in Moscow Univ. Math. Bull. 58 (2003), 20-23.

73) A. Giambruno and M. Zaicev, Codimension growth and minimal superalgebras, Trans. Amer. Math. Soc.355 (2003), 5091-5117.

74) A. Giambruno and C. Polcino Milies, Unitary units and skew elements in group algebras, Manuscripta Math. 111 (2003), 195-209.

75) A. Giambruno, Group actions codimensions and exponential behaviour, Ring Theory: Polynomial Identities and Combinatorial Methods, Lecture Notes in Pure and Appl. Math., 235, Marcel Dekker, New York, 2003, 287-310.

76) F. Benanti, A. Giambruno and M. Pipitone, Polynomial identities on superalgebras and exponential growth, J. Algebra 269 (2003), 422-438.

77) F. Benanti, A. Giambruno and I. Sviridova, Asymptotics for the multiplicities in the cocharacters of some PI-algebras, Proc. Amer. Math. Soc. 132 (2004), 669-679.

78) A. Giambruno C. Polcino Milies, Group identities on unit groups of group algebras, Rings, modules, algebras, and abelian groups, 219--227, Lecture Notes in Pure and Appl. Math.,236, Dekker, New York, 2004.

79) A. Giambruno and D. La Mattina, PI-algebras with slow codimension growth, J. Algebra 284 (2005), 371-391.

80) A. Giambruno, C. Polcino Milies, Free groups and involutions in the unit group of a group algebra, Arch. Math. (Basel) 84 (2005), no. 3, 205-210.

81) A. Giambruno, S. Mishchenko and M. Zaicev, Algebras with intermediate growth of the codimensions, Adv. Appl. Math. 37 (2006), no. 3, 360-377.

82) A. Giambruno, D. La Mattina and P. Misso, Polynomial identities on superalgebras: classifying linear growth, J. Pure Appl. Algebra 207 (2006), no. 1, 215-240.

83) A. Giambruno, D. La Mattina and P. Misso, On algebras and superalgebras with linear codimension growth; Groups, Rings and Group Rings, 173-182, Lecture Notes in Pure and Appl. Math. Vol. 248, Taylor and Francis, New York, 2006.

84) A. Giambruno, S. Mishchenko and M. Zaicev, On the growth of the identities of algebras, Algebra Discrete Math. 2 (2006), 50-61.

85) A. Giambruno and V. Petrogradsky, Poisson identities of enveloping algebras, Arch. Math. (Basel), 87 (2006), 505—515.

86) A. Giambruno and S. K. Sehgal, Group algebras whose Lie algebra of skew-symmetric elements is nilpotent, Groups, Rings and Algebras, 113-120, Contemporary Mathematics Vol. 420, Amer. Math. Soc., Providence R.I., 2006.

87) A. Giambruno and M. Zaicev, Multialternating Jordan polynomials and codimension growth of matrix algebras, Linear Algebra Appl. 422 (2007), 372-379.

88) A. Giambruno, D. La Mattina and V. Petrogradsky, Matrix algebras of polynomial codimension growth, Israel J. Math. 158 (2007), 367-378.

89) A. Giambruno, S. Mishchenko and M. Zaicev, Codimension growth of two-dimensional non-associative algebras, Proc. Amer. Math. Soc. 135, no. 11 (2007), 3405-3415.

90) A. Giambruno, S. Mishchenko and M. Zaicev, Codimensions of algebras and growth functions, Adv. Math. 217, No. 3 (2008), 1027-1052.

91) Y. Bahturin and A. Giambruno, Group gradings on associative algebras with involution, Canad. Math. Bull. 51 (2) (2008), 182-194.

92) A. Giambruno and M. Zaicev, Lie, Jordan and proper codimensions of associative algebras, Rend. Circ. Mat. Palermo 57 (2008), 161-171.

93) A A. Giambruno and M. Zaicev, Proper identities, Lie identities and exponential codimension growth, J. Algebra 320 (2008), 1933-1962.

94) A. Giambruno, C. Polcino Milies and S. K. Sehgal, Lie properties of symmetric elements in group rings, J. Algebra 321 (2009), 890-902.

95) A. Giambruno and S. Mishchenko, Super-cocharacters, star-cocharacters and multiplicities bounded by one, Manuscripta Math. 128 (2009), 483-504.

96) Giambruno, S. Mishchenko and M. Zaicev, Polynomial identities of algebras of small dimension, Comm Algebra 37 (2009), 1934-1948.

97) A. Giambruno, C. Polcino Milies and S. K. Sehgal, Group identities on symmetric units, J. Algebra 322 (2009), no. 8, 2801-2815.

98) A. Giambruno and S. Mishchenko, Polynomial growth of the codimensions: a characterization, Proc. Amer. Math. Soc. 138 (2010), 853-859.

99) A. Giambruno and M. Zaicev, Codimension growth of special simple Jordan algebras, Trans. Amer. Math. Soc. 362 (2010), 3107-3123.

100) A. Giambruno, C. Polcino Milies and S. K. Sehgal, Group algebras of torsion groups and Lie nilpotence, J. Group Theory 13 (2010), 221-231.

101) A. Giambruno and D. La Mattina, Graded polynomial identities and codimensions: computing the exponential growth, Adv. Math 225 (2010), 859–881.

102) A. Giambruno and G. Leal, Central units, class sums and characters of the symmetric group, Comm. Algebra 38 (2010), 3889-3896.

103) A. Giambruno, C. Polcino Milies and S. K. Sehgal, Star-group identities and groups of units, Arch. Math. 95 (2010), 501-508.

104) E. Aljadeff, A. Giambruno and D. La Mattina, Graded polynomial identities and exponential growth, J. Reine Angew. Math. 650 (2011), 83-100.

105) A. Giambruno, I. Shestakov and M. Zaicev, Finite dimensional nonassociative algebras and codimension growth, Adv. Appl. Math. 47 (2011), 125-139.

106) A. Giambruno and E. Zelmanov, On growth of codimensions of Jordan algebras, Groups, Algebras and Applications 205-210, Contemp. Math. Vol. 537 American Mathematical Society, Providence R.I., 2011.

107) A. Giambruno and A. Regev, Standard polynomials are characterized by their degree and exponent, J. Algebra 335 (2011), 74-82.

108) A. Giambruno and M. Zaicev, On codimension growth of finite dimensional Lie superalgebras, J. London Math. Soc. (2) 85 (2012), no. 2, 534–548.

109) A. Giambruno, S. Mishchenko, and M. Zaicev, Some numerical invariants of multilinear identities, Serdica Math. J. 38 (2012), no. 1-3, 371–394.

110) A. Giambruno, C. Polcino Milies and S. K. Sehgal, Group algebras and Lie nilpotence, J. Algebra 373 (2013), 276–283.

111) A. Cirrito and A. Giambruno, Group graded algebras and multiplicities bounded by a constant, J. Pure Appl. Algebra 217 (2013), no. 2, 259–268.

112) A. Giambruno and M. da Silva Souza, Graded polynomial identities and Specht property of the Lie algebra sl2, J. Algebra 389 (2013), 6–22.

113) E. Aljadeff and A. Giambruno, Multialternating graded polynomials and growth of polynomial identities, Proc. Amer. Math. Soc. 141 (2013), no. 9, 3055–3065.

114) S. Aquè and A. Giambruno, Cocharacters of bilinear mappings and graded matrices, Algebra Represent. Theory 16 (2013), no. 6, 1621–1646.

115) A. Giambruno and M. Zaicev, Non-integrality of the PI-exponent of special Lie algebras, Adv. Appl. Math. 51 (2013), no. 5, 619–634.

116) A. Giambruno and M. da Silva Souza, Minimal varieties of graded Lie algebras of exponential growth and the special Lie algebra sl2, J. Pure Appl. Algebra 218 (2014), no. 8, 1517–1527.

117) A. Giambruno, D. La Mattina and M. Zaicev, Classifying the Minimal Varieties of Polynomial Growth, Canad. J. Math. 66 (2014), no. 3, 625–640.

118) A. Giambruno and M. Zaicev, Growth of polynomial identities: is the sequence of codimensions eventually non-decreasing?, Bull. Lond. Math. Soc. 46 (2014), no. 4, 771–778.

119) A. Giambruno and M. Zaicev, Asymptotic growth of codimensions sequences of identities of associative algebras, Moscow Univ. Math. Bull. 69 (2104), 125-127.

120) A. Belov-Kanel, A. Giambruno, L. H. Rowen and U. Vishne, Zariski Closed Algebras in Varieties of Universal Algebra, Algebr. Represent. Theory 17 (2014), no. 6, 1771-1783.

121) A. Giambruno and M. Zaicev, Anomalies on codimension growth of algebras, Forum Math. 28 (2016), no. 4, 649–656.

122) A. Giambruno , A. Ioppolo and D. La Mattina, Varieties of Algebras with Superinvolution of Almost Polynomial Growth, Algebr. Represent. Theory 19 (2016), no. 3, 599–611.

123) A. Giambruno and S. Mishchenko, Degrees of irreducible characters of the symmetric group and exponential growth, Proc. Amer. Math. Soc. 144 (2016), no. 3, 943–953.

124) A. Giambruno, R. B. dos Santos and A. C. Vieira, Identities of *-superalgebras and almost polynomial growth, Linear Multilinear Algebra 64 (2016), no. 3, 484-501.

125) A. Giambruno, A. Ioppolo and F. Martino, Standard polynomials and matrices with superinvolutions, Linear Algebra Appl. 504 (2016), 272–291.

126) A. Giambruno and M. Zaicev, Polynomial identities and algebraic combinatorics on words, São Paulo J. Math. Sci. 10 (2016), no. 2, 219–227.

127) A. Giambruno, C. Polcino Milies and A. Valenti, Star-polynomial identities: computing the exponential growth of the codimensions, J. Algebra 469 (2017), 302–322.

128) A. Giambruno, S. Mishchenko, A. Valenti and M. Zaicev, Polynomial codimension growth and the Specht problem, J. Algebra 469 (2017), 421–436.

129) E. Aljadeff, A. Giambruno and Y. Karasik, Polynomial identities with involution, superinvolutions and the Grassmann envelope. Proc. Amer. Math. Soc. 145 (2017), no. 5, 1843–1857.

130) A. Giambruno, C. Polcino Milies and S. K. Sehgal, Star-group identities on units of group algebras: The non-torsion case, Forum Math. 30 (2018) no. 1, 213–225.

131) A. Giambruno and M. Zaicev, Sturmian words and overexponential codimension growth, Adv. in Appl. Math. 95 (2018), 53-64.

132) A. Giambruno, C. Polcino Milies and A. Valenti, Cocharacters of group graded algebras and multiplicities bounded by one, Linear Multilinear Algebra 66 (2018), no. 8, 1709–1715.

133) A. Giambruno and M. Zaicev, Central polynomials and growth functions, Israel J. Math. 226 (2018), no. 1, 15–28.

134) A. Giambruno, S. Mishchenko and M. Zaicev, Non integral exponential growth of central polynomials, Arch. Math. (Basel) 112 (2019), 149-160.

135) A. Giambruno and M. Zaicev, Central polynomials of associative algebras and their growth, Proc. Amer. Math. Soc. 147 (2019), 909-919.

136) A. Giambruno and C. Rizzo, Differential identities, 2 x 2 upper triangular matrices and varieties of almost polynomial growth, J. Pure Appl. Algebra 223 (2019), 1710-1727.

137) A. Giambruno, A. Ioppolo and D. La Mattina, Superalgebras with involution or superinvolution and almost polynomial growth of the codimensions, Algebr. Represent. Theory 22 (2019), no. 4, 961-976.

138) A. Giambruno, C. Polcino Milies and M. Zaicev, A characterization of fundamental algebras through S_n-characters, J. Algebra 541 (2020), 51-60.

139) A. Giambruno and M. Zaicev, Codimension growth of central polynomials of Lie algebras, Forum Math. 32 (2020), 201-206.

140) A. Giambruno, D. La Mattina and C. Polcino Milies, Star-fundamental algebras: polynomial identities and asymptotics, Trans. Amer. Math. Soc. (to appear).

141) A. Giambruno and D. La Mattina, Codimensions of star-algebras and low exponential growth, Israel J. Math. (to appear).

Books

1) A. Giambruno ed., “Recent developments in the theory of algebras with polynomial identities”, Suppl. Rend. Circ. Mat. Palermo II Vol. 31, 1993.

2) V. Drensky, A. Giambruno and S. K. Sehgal eds., “Methods in Ring Theory”, Lecture Notes in Pure and Applied Mathematics Vol. 198, Marcel Dekker, New York, 1998.

3) A. Giambruno, A. Regev and M. Zaicev eds., “Polynomial Identities and Combinatorial Methods”, Lecture Notes in Pure and Applied Mathematics, Vol. 235, Marcel Dekker, New York, 2003.

4) A. Giambruno and M. Zaicev, “Polynomial Identities and Asymptotic Methods”, Mathematical Surveys and Monographs Vol. 122, American Mathematical Society, Providence R.I., 2005.

5) A. Giambruno, C. Polcino Milies and S. K. Sehgal eds., “Groups, Rings and Group Rings”, Lecture Notes in Pure and Applied Mathematics, Vol. 248, Taylor and Francis, New York, 2006.

6) A. Giambruno, C. Polcino Milies and S. K. Sehgal eds., “Groups, Rings and Group Rings”. Contemporary Mathematics, Vol. 499, American Mathematical Society, Providence, R.I.,2009.

7) E. Aljadeff, A. Giambruno, C. Procesi and A. Regev, "Rings with polynomial identities and finite dimensional representations of algebras", Colloquium Publications, American Mathematical Society, Providence R.I. (to appear).