Publications of Martin Lorenz

Books and Lecture Notes



Gelfand-Kirillov Dimension and Poincaré Series

Cuadernos de Algebra, No. 7,
Universidad de Granada, 68 pp., 1988.



Multiplicative Invariant Theory

Encyclopaedia of Mathematical Sciences, Vol. 135,
subseries ``Invariant Theory and Algebraic Transformation Groups",
177 pp., Springer-Verlag, 2005. ISBN 3-540-24323-2

Table of contents       Corrections and updates (latest change Oct. 17, 2008)

Articles

  1. Primitive ideals of group algebras of supersoluble groups. Math. Annalen 225, 115-122 (1977).

  2. Completely prime primitive ideals in group algebras of finitely generated nilpotent-by-finite groups. Comm. in Algebra 6, 717-734 (1978).

  3. Primitive ideals in crossed products and rings with finite group actions. Math. Zeitschr. 158, 285-294 (1978).

  4. (with D. S. Passman) Centers and prime ideals in group algebras of polycyclic-by-finite groups. J. Algebra 57, 355-386 (1979).

  5. The heart of prime ideals in Ore extensions. Manuscripta math. 28, 293-304 (1979).

  6. Analogs of Clifford's theorem for polycyclic-by-finite groups. Trans. Amer. Math. Soc. 254, 295-317 (1979).

  7. (with G. Michler) On maximal ideals in Ore extensions. In: Ring Theory, Proceedings of the 1978 Antwerp Conference, pp. 139-151. Marcel Dekker, New York, 1979.

  8. (with D. S. Passman) Prime ideals in crossed products of finite groups. Israel J. Math. 33, 89-132 (1979).

  9. (with D. S. Passman) Integrality and normalizing extensions of rings. J. Algebra 61, 289-297 (1979).

  10. (with D. S. Passman) Observations on crossed products and fixed rings. Comm. in Algebra 8, 743-779 (1980).

  11. (with D. S. Passman) Prime ideals in group algebras of polycyclic-by-finite groups. Proc. London Math. Soc. (3) 43, 520-543 (1981).

  12. (with D. S. Passman) Two applications of Maschke's theorem. Comm. in Algebra 8, 1853-1866 (1980).

  13. (with D. S. Passman) Addendum-Prime ideals in crossed products of finite groups. Israel J. Math. 35, 311-322 (1980).

  14. Finite normalizing extensions of rings. Math. Zeitschr. 176, 447-484 (1981).

  15. Prime ideals in group algebras of polycyclic-by-finite groups: Vertices and sources. In: Séminaire d'algèbre P. Dubreil et M. P. Malliavin, Lect. Notes in Mathematics No. 867, pp. 406-420, Springer, Berlin-Heidelberg-New York, 1981.

  16. Completely prime ideals in Ore extensions. Comm. in Algebra 9, 1227-1232 (1981).

  17. Chains of prime ideals in enveloping algebras of solvable Lie algebras. J. London Math. Soc. (2) 24, 205-210 (1981).

  18. (with S. Montgomery and L. W. Small) Prime ideals in fixed rings II. Comm. in Algebra 10, 449-455 (1982).

  19. (with L. W. Small) On the Gelfand-Kirillov dimension of Noetherian PI-algebras. In: Amitsur, Saltman, Seligman (eds.), Algebraists' Homage: Papers in Ring Theory and Related Topics, Contemporary Mathematics 13, 199-205 (1982).

  20. The Goldie rank of prime supersolvable group algebras. Mitteilungen aus dem Math. Seminar Giessen 149, 115-129 (1981).

  21. On the Gelfand-Kirillov dimension of skew polynomial rings. J. Algebra 77, 186-188 (1982).

  22. Division algebras generated by finitely generated nilpotent groups. J. Algebra 85, 368-381 (1983).

  23. On the transcendence degree of group algebras of nilpotent groups. Glasgow Math. J. 25, 167-174 (1984).

  24. Group rings and division rings. In: F. van Oystaeyen (ed.), Methods in Ring Theory, pp. 265-280, D. Reidel Publ. Co., Dordrecht, 1984.

  25. On the cohomology of polycyclic-by-finite groups. J. Pure and Appl. Algebra 40, 87-98 (1986).

  26. (with M. Laska) Rational points on elliptic curves over Q in elementary abelian 2-extensions of Q. J. reine u. angew. Math. 355, 163-172 (1985).

  27. On Loewy lengths of projective modules for p-solvable groups. Comm. in Algebra 13, 1193-1212 (1985).

  28. K0 of skew group rings and simple Noetherian rings without idempotents. J. London Math. Soc. (2) 32, 41-50 (1985).

  29. On free subalgebras of certain division algebras. Proc. Amer. Math. Soc. 98, 401-405 (1986).

  30. On affine algebras. In: F. van Oystaeyen (ed.), Ring Theory, Lect. Notes in Mathematics No. 1197, pp. 121-126. Springer, Berlin-Heidelberg-New York, 1986.

  31. (with K.A. Brown and J. Howie) Induced resolutions and Grothendieck groups of polycyclic-by-finite groups. J. Pure and Appl. Algebra 53, 1-14 (1988).

  32. On the numerical local Langlands conjecture (after Koch and Zink). Contemporary Mathematics 86, 57-63 (1989).

  33. Frobenius reciprocity and G0 of skew group rings. In: J.L. Bueso, P. Jara, B. Torrecillas (eds.), Ring Theory, Lect. Notes in Mathematics No. 1328, pp. 165-172, Springer, Berlin-Heidelberg-New York, 1988.

  34. On Gelfand-Kirillov dimension and related topics. J. Algebra 118, 423-437 (1988).

  35. (with D. S. Passman) The structure of G0 for certain polycyclic group algebras and related algebras. Contemporary Mathematics 93, 283-302 (1989).

  36. Goldie ranks of prime polycyclic crossed products. In: F. van Oystaeyen and L. LeBruyn (eds.), Perspectives in Ring Theory, pp. 215-219, Kluwer Academic Publ., Dordrecht, 1988.

  37. The rank of G0 for polycyclic group algebras. In: S. Balcerzyk et al. (eds.), Topics in Algebra (Part 1), Banach Center Publications, Vol. 26, pp. 45-53, PWN, Warsaw, 1990.

  38. On the global dimension of fixed rings. Proc. Amer. Math. Soc. 106, 923-932 (1989).

  39. Crossed products: characters, cyclic homology, and Grothendieck groups. In: M. S. Montgomery and L. W. Small (eds.), Noncommutative Rings, MSRI Publications, Vol. 24, pp. 69-98, Springer, New York, 1992.

  40. (with K.A. Brown) Colimits of functors, and Grothendieck groups of infinite group algebras. In: L. Fuchs et al. (eds.), Abelian groups and noncommutative rings: A collection of papers in memory of Robert B. Warfield, Jr., Contemporary Mathematics 130, 89-109 (1992).

  41. On the homology of graded algebras. Comm. in Algebra 20, 489-507 (1992).

  42. (with K.A. Brown) Grothendieck groups of invariant rings and of group rings. J. Algebra 166, 423-454 (1994).

  43. (with K.A. Brown) Grothendieck groups and higher class groups of commutative invariants. In: L. A. Bokut et al. (eds.), Proceedings of the Second International Conference on Algebra. Dedicated to the memory of A. I. Shirshov. Contemporary Mathematics 184, 59-74 (1995).

  44. (with K.A. Brown) Grothendieck groups of invariant rings: filtrations. Proc. London Math. Soc. 67, 516-546 (1993).

  45. (with K.A. Brown) Grothendieck groups of invariant rings: examples. Comm. in Algebra 22, 279-306 (1994).

  46. (with M. E. Lorenz) On crossed products of Hopf algebras. Proc. Amer. Math. Soc. 123, 33-38 (1995).

  47. (with K.A. Brown) Grothendieck groups of invariant rings: linear actions of finite groups. Math. Zeitschr. 221, 113-137 (1996).

  48. (with M. E. Lorenz) Observations on crossed products and invariants of Hopf algebras. Archiv der Mathematik 63, 119-127 (1994).

  49. On Galois descent for Hochschild and cyclic homology. Comment. Math. Helv. 69, 474-482 (1994).

  50. Class groups of multiplicative invariants. J. Algebra 177, 242-254 (1995).

  51. Representations of finite dimensional Hopf algebras. J. Algebra 188, 476-505 (1997).

  52. Regularity of multiplicative invariants. Comm. in Algebra 24, 1051-1055 (1996).

  53. Picard groups of multiplicative invariants. Comment. Math. Helv. 72, 389-399 (1997).

  54. On the class equation for Hopf algebras. Proc. Amer. Math. Soc. 126, 2841-2844 (1998).

  55. K0 of invariant rings and nonabelian H1. J. Algebra 214, 458-478 (1999).

  56. (with Ed Letzter) Polycyclic-by-finite group algebras are catenary. Math. Res. Lett. 6, 183-194 (1999).

  57. Multiplicative invariants and semigroup algebras. Algebras and Representation Theory 4, 293-304 (2001).

  58. (with Nicole Lemire) On certain lattices associated with generic division algebras. J. Group Theory 3, 385-405 (2000).

  59. (with J. Pathak) On Cohen-Macaulay rings of invariants. J. Algebra 245, 247-264 (2001).

  60. (with Z. Reichstein, L.H. Rowen, and D.J. Saltman) Fields of definition of division algebras. J. London Math. Soc. 68, 651-670 (2003).

  61. On Euler classes of abelian-by-finite groups. J. Group Theory 6, 195-207 (2003).

  62. On the Cohen-Macaulay property of multiplicative invariants. Trans. Amer. Math. Soc. 358, 1605-1617 (2006).

  63. (with R. Guralnick) Orders of finite groups of matrices. In: ``Groups, Rings and Algebras: Proceedings of a Conference in Honor of Donald S. Passman'', Contemporary Mathematics 420, 141-162 (2006).

  64. (with Phùng Hô Hai) Koszul algebras and the quantum MacMahon Master Theorem. Bull. London Math. Soc. 39, 667-676 (2007).

  65. (with Phùng Hô Hai and Benoit Kriegk) N-homogeneous superalgebras. Journal of Noncommutative Geometry 2, 1-51 (2008).

  66. Group actions and rational ideals. Algebra and Number Theory 2, 467-499 (2008).

  67. Algebraic group actions on noncommutative spectra. Transformation Groups (to appear).