Publications of David Towers

Book:

1. David A. Towers:
A Guide To Linear Algebra.
Macmillans (1987).

I am the Consultant Editor for the series originally called the Macmillan Guides, now the Palgrave Macmillan Mathematical Guides , and in their second edition.

Ph. D. Thesis:

2. David A. Towers:
A Frattini Theory For Algebras.
University of Leeds (1972).

Published articles:

3. David A. Towers:
On The Generators Of A Nilpotent Nonassociative Algebra.
Quart. J. Math. Oxford (2) 22 (1971) 545-550.
4. David A. Towers:
On Elementary Lie Algebras.
J. London Math. Soc. (2) 7 (1973) 295-302.
5. David A. Towers:
A Frattini Theory For Algebras.
Proc. London Math. Soc. (3) 27 (1973) 440-462.
6. Ian Stewart, David A. Towers:
The Frattini Subalgebras Of Certain Infinite-Dimensional Lie Algebras.
J. London Math. Soc. (2) 11 (1975) 207-215.
7. David A. Towers:
Dualisms Of Lie Algebras.
J. Algebra 59 (1979) 490-495.
8. David A. Towers:
Lie Algebras, All Of Whose Proper Subalgebras Are Nilpotent.
Linear Algebra Appl. 32 (1980) 61-73.
9. David A. Towers:
Dimension Preserving Lattice Isomorphisms Of Lie Algebras.
Comm. Alg. 8 (1980) 1371-1386.
10. David A. Towers:
Two Ideals Of A Lie Algebra Closely Related To Its Frattini Ideal (dedicated To Professor W. Gaschutz on his 60th birthday).
Arch. Math. 35 (1980) 112-120.
11. David A. Towers:
On Complemented Lie Algebras.
J. London Math. Soc. (2) 22 (1980) 63-65.
12. David A. Towers:
On Lie Algebras In Which Modular Pairs Of Subalgebras Are Permutable.
J. Algebra 68 (1981) 369-377.
13. David A. Towers:
Lattice Isomorphisms Of Lie Algebras.
Math. Proc. Camb. Phil. Soc. 89 (1981) 285-292.
14. David A. Towers:
Lie Algebras, All Of Whose Maximal Subalgebras Have Codimension One.
Proc. Edin. Math. Soc. 24 (1981) 217-219.
15. David A. Towers:
Frattini Embeddings Of Ideals In Modular Lie Algebras.
Arch. Math. 43 (1984) 121-123.
16. David A. Towers:
Lattice Isomorphisms Of Lie Algebras (Addendum).
Math. Proc. Camb. Phil. Soc. 95 (1984) 511-512.
17. J. Baylis, N. Forrest, R. Haggarty, J. Hebborn, V.Petrov,R. Ranzetta, D. A. Towers:
Perennial Difficulties In Mathematics.
Proceedings Of The Undergraduate Mathematics Teaching Conference, Shell Centre For Mathematical Education, University Of Nottingham (1984).
18. David A. Towers:
On Ideally Finite Lie Algebras Which Are Lower Semi-Modular.
Proc. Edin. Math. Soc. 28 (1985) 9-11.
19. David A. Towers:
Problems Faced By Mathematics Students At The School/Higher Education Interface.
Math. Gazette 69 (1985) 180-187.
20. David A. Towers:
Minimal Non- Supersolvable Lie Algebras.
Algebras, Groups And Geometries 2 (1985) 1-9.
21. Mark Lincoln, David A. Towers:
Frattini Theory For Restricted Lie Algebras.
Arch. Math. 45 (1985) 451-457.
22. K. Austin, N. Bibby, M. Dwan, C. Houghton, M. Keating, D. Quadling, D.A.Towers and C. Whitehead:
Experiment And Intuition In Pure Mathematics.
Proceedings Of The Undergraduate Mathematics Teaching Conference, Shell Centre For Mathematical Education, University Of Nottingham (1985).
23. David A. Towers:
Semi-Modular Subalgebras Of A Lie Algebra.
J. Algebra 103 (1986) 202-207.
24. David A. Towers:
Lattice Automorphisms Of Lie Algebras.
Arch. Math. 46 (1986) 39-43.
25. David A. Towers:
Nonassociative Algebraic Structures Arising In Genetics.
Math. Gazette 70 (1986) 281-286.
26. David A.Towers:
The Role Of Mathematics Education Courses In Undergraduate Mathematics Teaching.
paper delivered at the International Congress Of Mathematicians, Berkeley, August 3 - 11(1986).
27. K. Austin, C.Davies, K. Houston, P. Oates, P. Surgey, M. Thornlinson and D.A.Towers:
What Balance Of Learning Activities Do Mathematics Students Need?.
Proceedings Of The Undergraduate Mathematics Teaching Conference, Shell Centre For Mathematical Education, University Of Nottingham (1986).
(pdf)
28. David A.Towers:
Proceedings Of The Undergraduate Mathematics Teaching Conference, Shell Centre For Mathematical Education, University Of Nottingham (1986).
Editor.
29. David A. Towers:
Almost Nilpotent Lie Algebras.
Glasgow Math, J. 29 (1987) 7-11.
30. David A.Towers:
Proceedings Of The Undergraduate Mathematics Teaching Conference, Shell Centre For Mathematical Education, University Of Nottingham (1987).
Editor.
31. David A.Towers:
Proceedings Of The Undergraduate Mathematics Teaching Conference, Shell Centre For Mathematical Education, University Of Nottingham (1988).
Editor.
32. David A. Towers, Peter R. Turner:
A Flexible First Year Undergraduate Mathematics Curriculum.
Int. J. Math. Educ. Sci. Technol. 20 (1989) 469-473.
33. Kevin Bowman, David A. Towers:
Modularity Conditions In Lie Algebras.
Hiroshima Math. J. 19 (1989) 333-346.
34. David A.Towers:
Proceedings Of The Undergraduate Mathematics Teaching Conference, Shell Centre For Mathematical Education, University Of Nottingham (1990).
Editor.
35. Kevin Bowman, David A. Towers:
On Lie Algebras In Which Modular Pairs Are Permutable II.
University Of Lancaster Report (1994)
36. David A. Towers:
Lie Algebras Whose Maximal Subalgebras Are Modular*.
Algebras, Groups And Geometries 12 (1995) 89-98.
37. Kevin Bowman, David A. Towers:
On Almost Nilpotent-By-Abelian Lie Algebras.
Lin. Algebra Appl. 247 (1996) 159-167.
38. Kevin Bowman, David A. Towers:
On Power Associative Bernstein Algebras Of Arbitrary Order.
Algebras, Groups And Geometries 13 (1996) 295-322.
(postscript, pdf)
39. Kevin Bowman, David A. Towers:
Higher Order Bernstein Algebras Given By Symmetric Bilinear Forms.
Lin. Algebra Appl. 252 (1997) 71-79.
40. Mark Lincoln, David A. Towers:
The Frattini Subalgebra Of A Solvable Lie Algebra.
Proc. Edin. Math. Soc. 40 (1997) 31-40.
41. David A. Towers:
On Modular* Subalgebras Of A Lie Algebra.
J. Algebra 190 (1997) 461-473.
42. David A. Towers:
Higher Order Jordan Bernstein Algebras.
Algebras, Groups And Geometries (1998).
(postscript, pdf)
43. Kevin Bowman, David A. Towers, Vicente R. Varea:
On Lie Algebras All Of Whose Minimal Subalgebras are Lower Modular.
Comm. Algebra 32(12) (2004) 4515-4533.
44. Kevin Bowman, David A. Towers, Vicente R. Varea:
On Upper Modular Subalgebras Of A Lie Algebra.
Proc. Edin. Math. Soc. 47(2) (2004) 325-337.
45. David A. Towers, Vicente R. Varea:
Elementary Lie Algebras and Lie A-Algebras.
J. Algebra 312 (2007) 891-901.
(postscript, pdf)
46. Kevin Bowman, David A. Towers, Vicente R. Varea:
On Flags And Maximal Chains Of Lower Modular Subalgebras Of Lie Algebras.
J. Lie Theory 17 (2007) 605616.
(electronic version)
47. Kevin Bowman, David A. Towers, Vicente R. Varea:
Two Generator Subalgebras Of Lie Algebras.
Linear Multilinear Algebra 55(5) (2007) 429-438.
(postscript, pdf)
48. David A. Towers:
On Semimodular Subalgebras Of Lie Algebras Over Fields Of Arbitrary Characteristic.
Asian-European J. Math. 1(2) (2008) 283-294.
(postscript, pdf)
49. David A. Towers:
C-Supplemented Subalgebras Of Lie Algebras.
J. Lie Theory 18 (2008) 717-724.
(electronic version)
50. David A. Towers:
C-Ideals of Lie Algebras.
Comm. Alg. 37 (2009) 4366-4373.
(postscript, pdf)
51. David A. Towers:
The index complex of a maxmal subalgebra of a Lie algebra.
Proc. Edin. Math. Soc. 54 (2) (2011) 531-542.
(postscript, pdf)
52. David A. Towers:
Solvable Lie A-Algebras.
J. Algebra 340 (1) (2011) 1-12.
(postscript, pdf)
53. David A. Towers:
On maximal subalgebras of Lie algebras containing Engel subalgebras.
J. Pure Appl. Algebra 216 (2012), 688-693.
(postscript, pdf)
54. David A. Towers:
Solvable complemented Lie algebras.
Proc. Amer. Math. Soc. 140 (2012), 3823-3830.
(postscript, pdf)
55. David A. Towers, Vicente R. Varea:
Further Results On Elementary Lie Algebras and Lie A-Algebras.
Comm. Alg. 41 (4) (2013), 1432-1441.
(postscript, pdf)
56. David A. Towers:
Complements of intervals and prefrattini subalgebras of solvable Lie algebras.
Proc. Amer. Math. Soc 141 (2013), 1893-1901.
(postscript, pdf)
57. David A. Towers:
Supplements to maximal subalgebras of Lie algebras.
Comm. Alg. 41 (10) (2013), 3848-3857.
(postscript, pdf)
58. Manuel Ceballos, David A. Towers:
On abelian subalgebras and ideals of maximal dimension in supersolvable Lie algebras.
J. Pure Appl. Algebra 218 (2014), 497-503
(pdf)
59. David A. Towers:
On conjugacy of maximal subalgebras of solvable Lie algebras.
Comm. Alg. 42 (3) (2014), 1350-1353
(postscript, pdf)
60. David A. Towers:
On the lengths of certain chains of subalgebras in Lie algebras.
Comm.Alg. 42 (2014), 4778-4789
(pdf)
61. David A. Towers:
On certain decompositions of solvable Lie algebras.
J. Lie Theory 24 (4) (2014), 969-978
(pdf)
62. David A. Towers:
On minimal non-elementary Lie algebras.
Proc. Amer. Math. Soc. 143 (2015), 117-120
(pdf )
63. David A. Towers:
C-sections of Lie algebras.
J. Algebra 427 (2015), 7684
(pdf)
64. David A. Towers:
Subalgebras that cover or avoid chief factors of Lie algebras.
Proc. Amer. Math. Soc. 143 (2015), 3377-3385
(pdf)
65. David A. Towers:
Maximal subalgebras and chief factors of Lie algebras.
J. Pure Appl. Algebra 220 (2016), 482-493
(pdf)
66. David A. Towers:
On n-maximal subalgebras of Lie algebras.
Proc. Amer. Math. Soc. 144 (2016), 1457-1466
(pdf)
67. David A. Towers:
Chief factors of Lie algebras.
J. Generalised Lie Theory Appl. S2 (2016) in memory of John Nash
(pdf)
68. David A. Towers:
The generalised nilradical of a Lie algebra.
J. Algebra 470 (2017), 197218
(pdf)
69. David A. Towers:
On maximal subalgebras and a generalised Jordan Holder Theorem for Lie algebras.
Comm. Alg. 45(3) (2017), 1284-1293
(pdf)
70. David A. Towers:
Lie algebras with nilpotent length greater than that of each of their subalgebras.
Algebras and Representation Theory 20 (3) (2017), 735-750
(pdf)
71. David A. Towers and Zekiye Ciloglu:
On complemented non-abelian chief factors of Lie algebras.
to appear in J. Lie Theory
(pdf)

Preprints:

72. David A. Towers and Zekiye Ciloglu:
C-subideals of Lie algebras.
in preparation