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Research

Professor David Towers

Emeritus

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  1. 2023
  2. Published

    Zinbiel algebras are Nilpotent

    Towers, D., 1/08/2023, In: Journal of Algebra and Its Applications. 22, 8, 5 p., 2350166.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  3. Published

    On the subalgebra lattice of a restricted Lie algebra

    Paez-Guillan, P., Siciliano, S. & Towers, D., 1/03/2023, In: Linear Algebra and its Applications. 660, p. 47-65 19 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  4. Published

    Abelian subalgebras and ideals of maximal dimension in Zinbiel algebras

    Ceballos, M. & Towers, D., 27/02/2023, In: Communications in Algebra. 51, 4, p. 1323-1333 11 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  5. 2022
  6. Published

    Abelian subalgebras and ideals of maximal dimension in supersolvable and nilpotent Lie algebras

    Towers, D., 30/09/2022, In: Linear and Multilinear Algebra. 70, 13, p. 2551-2568 18 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  7. Published

    On the subalgebra lattice of a Leibniz algebra

    Siciliano, S. & Towers, D., 31/01/2022, In: Communications in Algebra. 50, 1, p. 255-267 13 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  8. 2021
  9. Published

    On certain classes of algebras in which centralizers are ideals

    Towers, D. & Saha, R., 23/11/2021, In: Journal of Lie Theory. 31, 4, p. 991-1002 12 p.

    Research output: Contribution to Journal/Magazine › Journal article

  10. Published

    The nilradical of a Leibniz algebra

    Towers, D., 31/10/2021, In: Communications in Algebra. 49, 10, p. 4345-4347 3 p.

    Research output: Contribution to Journal/Magazine › Journal article

  11. Published

    Weak c-ideals of a Lie algebra

    Towers, D. & Ciloglu, Z., 16/09/2021, In: Turkish Journal of Mathematics. 45, 5, p. 1940-1948 9 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  12. Published

    Lattice isomorphisms of Leibniz algebras

    Towers, D., 15/07/2021, In: Journal of Algebra. 578, p. 421-432 12 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  13. Published

    Classes of algebras and closure operations

    Gutierrez, I., Torresblanca-Badillo, A. & Towers, D., 8/05/2021, In: Communications in Algebra. 49, 6, p. 2563-2577 15 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  14. 2020
  15. Published

    Editorial: Workshop on Nonassociative algebras and their applications

    Towers, D., 18/12/2020, Special Issue S1 ed. Glasgow Mathematical Journal. 2 p.

    Research output: Book/Report/Proceedings › Proceedings

  16. Published

    Leibniz A-algebras

    Towers, D., 11/10/2020, In: Communications in Mathematics. 28, 2, p. 103-121 19 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  17. Published

    Quasi-ideals of Leibniz algebras

    Towers, D., 28/08/2020, In: Communications in Algebra. 48, 11, p. 4569-4579 11 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  18. 2018
  19. Published

    On complemented non-abelian chief factors of Lie algebras

    Ciloglu, Z. & Towers, D. A., 1/07/2018, In: Journal of Lie Theory. 28, 2, p. 427-442 16 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  20. 2017
  21. Published

    Lie algebras with nilpotent length greater than that of each of their subalgebras

    Towers, D. A., 06/2017, In: Algebras and Representation Theory. 20, 3, p. 735-750 16 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  22. Published

    On maximal subalgebras and a generalised Jordan-Holder Theorem for Lie algebras

    Towers, D. A., 4/03/2017, In: Communications in Algebra. 45, 3, p. 1284-1293 10 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  23. Published

    The generalised nilradical of a Lie algebra

    Towers, D. A., 15/01/2017, In: Journal of Algebra. 470, p. 197-218 22 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  24. 2016
  25. Published

    Chief factors of Lie Algebras

    Towers, D. A., 7/01/2016, In: Journal of Generalized Lie Theory and Applications. S2, 3 p.

    Research output: Contribution to Journal/Magazine › Editorial › peer-review

  26. Published

    Maximal subalgebras and chief factors of Lie algebras

    Towers, D., 01/2016, In: Journal of Pure and Applied Algebra. 220, 1, p. 482-493 12 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  27. Published

    On n-maximal subalgebras of Lie algebras

    Towers, D., 01/2016, In: Proceedings of the American Mathematical Society. 144, 4, p. 1457-1466 10 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  28. 2015
  29. Published

    C-sections of Lie algebras

    Towers, D., 1/04/2015, In: Journal of Algebra. 427, p. 76-84 9 p.

    Research output: Contribution to Journal/Magazine › Journal article

  30. Published

    On minimal non-elementary Lie algebras

    Towers, D., 2015, In: Proceedings of the American Mathematical Society. 143, 1, p. 117-120 4 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  31. Published

    Subalgebras that cover or avoid chief factors of Lie algebras

    Towers, D., 2015, In: Proceedings of the American Mathematical Society. 143, 8, p. 3377-3385 9 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  32. 2014
  33. Published

    On certain decompositions of solvable Lie algebras

    Towers, D., 12/2014, In: Journal of Lie Theory. 24, 4, p. 969-978 10 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  34. Published

    On abelian subalgebras and ideals of maximal dimension in supersolvable Lie algebras

    Ceballos, M. & Towers, D., 03/2014, In: Journal of Pure and Applied Algebra. 218, 3, p. 497-503 16 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  35. Published

    On conjugacy of maximal subalgebras of solvable Lie algebras

    Towers, D., 03/2014, In: Communications in Algebra. 42, 3, p. 1350-1353 4 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  36. Published

    On the lengths of certain chains of subalgebras in Lie algebras

    Towers, D., 2014, In: Communications in Algebra. 42, 11, p. 4778-4789 12 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  37. 2013
  38. Published

    Supplements to maximal subalgebras of Lie algebras

    Towers, D. A., 10/2013, In: Communications in Algebra. 41, 10, p. 3848-3857 10 p.

    Research output: Contribution to Journal/Magazine › Journal article

  39. Published

    Complements of intervals and prefrattini subalgebras of solvable Lie algebras.

    Towers, D. A., 2013, In: Proceedings of the American Mathematical Society. 141, 6, p. 1893-1901 9 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  40. Published

    Further results on elementary Lie algebras and Lie A-algebras.

    Towers, D. A. & Varea, V. R., 2013, In: Communications in Algebra. 41, 4, p. 1432-1441 10 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  41. 2012
  42. Published

    Maximal subalgebras of Lie algebras containing Engel subalgebras.

    Towers, D. A., 03/2012, In: Journal of Pure and Applied Algebra. 216, 3, p. 688-693 6 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  43. Published

    Solvable complemented Lie algebras.

    Towers, D. A., 1/01/2012, In: Proceedings of the American Mathematical Society. 140, 11, p. 3823-3830 8 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  44. 2011
  45. Published

    Solvable Lie A-algebras.

    Towers, D. A., 15/08/2011, In: Journal of Algebra. 340, 1, p. 1-12 12 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  46. Published

    The index complex of a maximal subalgebra of a Lie algebra.

    Towers, D. A., 1/06/2011, In: Proceedings of the Edinburgh Mathematical Society. 54, 2, p. 531-542 12 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  47. 2009
  48. Published

    C-Ideals of Lie Algebras.

    Towers, D. A., 12/2009, In: Communications in Algebra. 37, 12, p. 4366-4373 8 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  49. 2008
  50. Published

    On semi-modular subalgebras of Lie algebras over fields of arbitrary characteristic.

    Towers, D. A., 06/2008, In: Asian-European Journal of Mathematics. 1, 2, p. 283-294 12 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  51. Published

    C-Supplemented Subalgebras of Lie Algebras.

    Towers, D. A., 2008, In: Journal of Lie Theory. 18, 3, p. 717-724 8 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  52. 2007
  53. Published

    Two Generator Subalgebras Of Lie Algebras.

    Bowman, K., Towers, D. A. & Varea, V. R., 09/2007, In: Linear and Multilinear Algebra. 55, 5, p. 429-438 10 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  54. Published

    Elementary Lie Algebras and Lie A-Algebras.

    Towers, D. A. & Varea, V. R., 15/06/2007, In: Journal of Algebra. 312, 2, p. 891-901 11 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  55. Published

    On Flags And Maximal Chains Of Lower Modular Subalgebras Of Lie Algebras.

    Bowman, K., Towers, D. A. & Varea, V. R., 2007, In: Journal of Lie Theory. 17, 3, p. 605-616 12 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  56. 2004
  57. Published

    On upper modular subalgebras of a Lie algebra.

    Bowman, K., Towers, D. A. & Varea, V. R., 1/06/2004, In: Proceedings of the Edinburgh Mathematical Society. 47, 2, p. 325-337 13 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  58. Published

    On Lie algebras all of whose minimal subalgebras are lower modular.

    Bowman, K., Towers, D. A. & Varea, V. R., 2004, In: Communications in Algebra. 32, 12, p. 4515-4533 19 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  59. 1997
  60. Published

    Higher-order Bernstein algebras given by symmetric bilinear forms

    Towers, D. & Bowman, K., 02/1997, In: Linear Algebra and its Applications. 252, 1-3, p. 71-79 9 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  61. Published

    On modular* subalgebras of a Lie algebra

    Towers, D., 1997, In: Journal of Algebra. 190, 2, p. 461-473 13 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  62. Published

    The Frattini p-subalgebra of a solvable Lie p-algebra

    Lincoln, M. & Towers, D., 1997, In: Proceedings of the Edinburgh Mathematical Society. 40, 1, p. 31-40 10 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  63. 1996
  64. Published

    On almost nilpotent-by-abelian Lie algebras.

    Bowman, K. & Towers, D. A., 1/11/1996, In: Linear Algebra and its Applications. 247, 1, p. 159-167 9 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  65. Published

    On power-associative Bernstein algebras of arbitrary order

    Towers, D., 1996, In: Algebras, Groups and Geometries. 13, p. 295-322 28 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  66. 1995
  67. Published

    Lie algebras whose maximal subalgebras are modular*

    Towers, D., 1995, In: Algebras, Groups and Geometries. 12, p. 89-98 10 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  68. 1989
  69. Published

    Making mathematics more attractive

    Bell, G., Clegg, D., Farwell, R., Hebborn, J., Houston, K., Lazenby, P., McCauley, G., McGough, J., Newton, E., Nicholson, D., Tanner, D. & Towers, D. A., 11/1989, Mathematics 16-20. Shell Centre for Mathematical Education, Nottingham University, p. 105-114 10 p.

    Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSN › Conference contribution/Paper › peer-review

  70. Published

    Modularity conditions in Lie algebras

    Towers, D. & Bowman, K., 07/1989, In: Hiroshima Mathematical Journal. 19, 2, p. 333-346 14 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  71. Published

    A flexible first year undergraduate mathematics curriculum

    Towers, D. & Turner, P., 1989, In: International Journal of Mathematical Education in Science and Technology. 20, 3, p. 469-473 5 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  72. 1987
  73. Published

    A Guide to Linear Algebra

    Towers, D., 1987, Palgrave Macmillan. 210 p. (Palgrave Guides)

    Research output: Book/Report/Proceedings › Book

  74. Published

    Almost nilpotent Lie algebras

    Towers, D., 1987, In: Glasgow Mathematical Journal. 29, 1, p. 7-11 5 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  75. 1986
  76. Published

    Semi-modular subalgebras of a Lie algebra

    Towers, D. A., 1/10/1986, In: Journal of Algebra. 103, 1, p. 202-207 6 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  77. Published

    The role of mathematics education courses in undergraduate mathematics teaching

    Towers, D., 08/1986. 0 p.

    Research output: Contribution to conference - Without ISBN/ISSN › Conference paper

  78. Published

    Lattice automorphisms of Lie algebras

    Towers, D., 1986, In: Archiv der Mathematik. 46, p. 39-43 5 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  79. Published

    Nonassociative structures arising in genetics

    Towers, D., 1986, In: Mathematical Gazette. 70, p. 281-286 6 p.

    Research output: Contribution to Journal/Magazine › Journal article

  80. Published

    What balance of learning activities do mathematics students need?

    Austin, K., Davies, C., Houston, K., Oates, P., Surgey, P., Thomlinson, M. & Towers, D., 1986, Proceedings of the Undergraduate Mathematics Teaching Conference 15 p.

    Research output: Contribution to specialist publication › Article

  81. 1985
  82. Published

    Experiment and Intuition in Pure Mathematics

    Towers, D., Austin, K., Bibby, N., Dwan, M., Houghton, C., Keating, M., Quadling, D. & Whitehead, C., 1985, In: Proceedings of the Undergraduate Mathematics Teaching Conference.

    Research output: Contribution to Journal/Magazine › Journal article

  83. Published

    Frattini theory for restricted Lie algebras

    Towers, D. & Lincoln, M., 1985, In: Archiv der Mathematik. 45, p. 451-457 7 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  84. Published

    Minimal non-supersolvable Lie algebras

    Towers, D., 1985, In: Algebras, Groups and Geometries. 2, p. 1-9 9 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  85. Published

    On ideally finite Lie algebras which are lower semi-modular

    Towers, D., 1985, In: Proceedings of the Edinburgh Mathematical Society. 28, p. 9-11 3 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  86. Published

    Problems faced by mathematics students at the school/higher education interface

    Towers, D., 1985, In: Mathematical Gazette. 69, p. 180-187 8 p.

    Research output: Contribution to Journal/Magazine › Journal article

  87. 1984
  88. Published

    Lattice isomorphisms of Lie algebras (addendum)

    Towers, D., 1/05/1984, In: Mathematical Proceedings of the Cambridge Philosophical Society. 95, 3, p. 511-512 2 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  89. Published

    Frattini embeddings of ideals in modular Lie algebras

    Towers, D., 1984, In: Archiv der Mathematik. 43, p. 121-123 3 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  90. Published

    Perennial difficulties in mathematics

    Baylis, J., Forrest, N., Haggarty, R., Hebborn, J., Petrov, V., Ranzetta, R. & Towers, D., 1984, Proceedings of the Undergraduate Mathematics Teaching Conference, p. 73-86 14 p.

    Research output: Contribution to specialist publication › Article

  91. 1981
  92. Published

    On Lie algebras in which modular pairs of subalgebras are permutable

    Towers, D., 02/1981, In: Journal of Algebra. 68, 2, p. 369-377 9 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  93. Published

    Lattice isomorphisms of Lie algebras

    Towers, D., 1981, In: Mathematical Proceedings of the Cambridge Philosophical Society. 89, p. 285-292 8 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  94. Published

    Lie algebras all of whose maximal subalgebras have codimension one

    Towers, D., 1981, In: Proceedings of the Edinburgh Mathematical Society. 24, p. 217-219 3 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  95. 1980
  96. Published

    Two ideals of an algebra closely related to its Frattini ideal

    Towers, D., 12/1980, In: Archiv der Mathematik. 35, 1, p. 112-120 9 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  97. Published

    On complemented Lie algebras

    Towers, D., 08/1980, In: Journal of the London Mathematical Society. 22, 1, p. 63-65 3 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  98. Published

    Dimension preserving lattice isomorphisms of Lie algebras

    Towers, D., 1980, In: Communications in Algebra. 8, 14, p. 1371-1386 16 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  99. Published

    Lie algebras all of whose proper subalgebras are nilpotent

    Towers, D., 1980, In: Linear Algebra and its Applications. 32, p. 61-73 13 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  100. 1979
  101. Published

    Dualisms of Lie algebras

    Towers, D., 08/1979, In: Journal of Algebra. 59, 2, p. 490-495 6 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  102. 1975
  103. Published

    The Frattini subalgebras of certain infinite-dimensional Lie algebras

    Towers, D. & Stewart, I., 09/1975, In: Journal of the London Mathematical Society. 11, 2, p. 207-215 9 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  104. 1973
  105. Published

    Elementary Lie algebras

    Towers, D., 11/1973, In: Journal of the London Mathematical Society. 7, 2, p. 295-302 8 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  106. Published

    A Frattini theory for algebras

    Towers, D., 09/1973, In: Proceedings of the London Mathematical Society. 27, 3, p. 440-462 23 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  107. 1971
  108. Published

    On the generators of a nilpotent nonassociative algebra

    Towers, D., 12/1971, In: The Quarterly Journal of Mathematics. 22, 4, p. 545-550 6 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

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