Science, Technology and Engineering

• Books
• Book Chapters
• Journal Articles: Mathematics
• Other Articles

Books

1. J. Pitkethly and B. Davey, Dualisability: Unary Algebras and Beyond, Springer, 2005. website
2. B. A. Davey and H. A. Priestley, Introduction to Lattices and Order, Second edition, Cambridge University Press, 2002. website
3. D. M. Clark and B. A. Davey, Natural Dualities for the Working Algebraist, Cambridge University Press, 1998. website
4. B. A. Davey and H. A. Priestley, Introduction to Lattices and Order, Cambridge University Press, 1990.

Book Chapters

5. B. A. Davey and H. A. Priestley, Distributive lattices and duality, General Lattice Theory (G. Grätzer), Second edition, Birkhäuser, 1998, pp. 499–517.
6. B. A. Davey and I. G. Rosenberg, Natural dualities and clones, Advances in Mathematical Sciences: CRM's 25 Years (Montreal, 1994) (L. Vinet, ed.), CRM Proc. Lecture Notes 11, Amer. Math. Soc., 1997, pp. 385–402.
7. B. A. Davey, Dualisability in general and endodualisability in particular, Logic and Algebra (Pontignano, 1994) (A. Ursini and P. Aglianò, eds), Lecture Notes in Pure and Appl. Math. 180, Dekker, 1996, pp. 437–455.
8. B. A. Davey and R. W. Quackenbush, Bookkeeping duality for paraprimal algebras, Contributions to General Algebra 9 (Linz, 1994) (H. K. Kaiser et al., eds), Hölder-Pichler-Tempsky, 1995, pp. 19–26.
9. B. A. Davey, Duality theory on ten dollars a day, Algebras and Orders (Montreal, 1991) (I. G. Rosenberg and G. Sabidussi, eds), NATO Adv. Sci. Inst. Ser. C: Math. Phys. Sci. 389, Kluwer, 1993, pp. 71–111.
10. B. A. Davey and H. Werner, Piggyback dualities, Lectures in Universal Algebra (Szeged, 1983) (L. Szabó and Á. Szendrei, eds), Colloq. Math. Soc. János Bolyai 43, North-Holland, 1986, pp. 61–83.
11. B. A. Davey and H. Werner, Dualities and equivalences for varieties of algebras, Contributions to Lattice Theory (Szeged, 1980) (A. P. Huhn and E. T. Schmidt, eds), Colloq. Math. Soc. János Bolyai 33, North-Holland, 1983, pp. 101–275.
12. B. A. Davey and D. Duffus, Exponentiation and duality, Ordered Sets (Banff, 1981) (I. Rival, ed.), NATO Adv. Study Inst. Ser. C: Math. Phys. Sci. 83, Reidel, 1982, pp. 43–95.
13. B. A. Davey, Topological duality for prevarieties of universal algebras, Studies in Foundations and Combinatorics (G.-C. Rota, ed.), Adv. in Math. Suppl. Stud. 1, Academic Press, 1978, pp. 61–99.

Journal Articles: Mathematics

14. D. M. Clark, B. A. Davey, M. Jackson and J. G. Pitkethly, The axiomatizability of topological prevarieties, Adv. Math., to appear. preprint
15. B. A. Davey, M. Jackson, M. Maróti and R. N. McKenzie, Principal and syntactic congruences in congruence-distributive and congruence-permutable varieties, J. Aust. Math. Soc., to appear. preprint
16. B. A. Davey, M. Haviar and H. A. Priestley, Boolean topological distributive lattices and canonical extensions, Appl. Categ. Structures 15 (2007), 225–241. preprint
17. B. A. Davey, M. Jackson, J. Pitkethly and M. R. Talukder, Natural dualities for semilattice-based algebras, Algebra Universalis 57 (2007), 463–490. preprint
18. D. M. Clark, B. A. Davey and R. Willard, Not every full duality is strong!, Algebra Universalis 57 (2007), 375–381. preprint
19. B. A. Davey, J. G. Pitkethly and R. Willard, Dualisability versus residual character: a theorem and a counterexample, J. Pure Appl. Algebra 210 (2007), 423–435. preprint
20. B. A. Davey, M. Haviar and T. Niven, When is a full duality strong?, Houston J. Math. 33 (2007), 1–22. preprint
21. B. A. Davey, M. Haviar, T. Niven and N. Perkal, Full but not strong dualities at the finite level: extending the realm, Algebra Universalis 56 (2007), 37–56. reprint
22. B. A. Davey, Natural dualities for structures, Acta Univ. M. Belii Ser. Math. 13 (2006), 3–28. preprint
23. B. A. Davey, M. Haviar and R. Willard, Structural entailment, Algebra Universalis 54 (2005), 397–416. reprint
24. B. A. Davey, M. Haviar and R. Willard, Full does not imply strong, does it?, Algebra Universalis 54 (2005), 1–22. reprint
25. B. A. Davey and M. R. Talukder, Dual categories for endodualisable Heyting algebras: optimization and axiomatization, Algebra Universalis 53 (2005), 331–355. reprint
26. D. M. Clark, B. A. Davey, R. S. Freese and M. Jackson, Standard topological algebras: syntactic and principal congruences and profiniteness, Algebra Universalis 52 (2004), 343–376. reprint
27. B. A. Davey and M. Haviar, Applications of Priestley duality in transferring optimal dualities, Studia Logica 78 (2004), 213–236. reprint
28. D. M. Clark, B. A. Davey, M. Haviar, J. G. Pitkethly and M. R. Talukder, Standard topological quasi-varieties, Houston J. Math. 29 (2003), 859–887. reprint
29. B. A. Davey and J. C. Galati, A coalgebraic view of Heyting duality, Studia Logica 75 (2003), 259–270. reprint
30. D. M. Clark, B. A. Davey and J. G. Pitkethly, The complexity of dualisability: three-element unary algebras, Internat. J. Algebra Comput. 13 (2003), 361–391. reprint
31. B. A. Davey and M. Haviar, Transferring optimal dualities: theory and practice, J. Aust. Math. Soc. 74 (2003), 393–420. preprint
32. B. A. Davey and M. R. Talukder, Functor category dualities for varieties of Heyting algebras, J. Pure Appl. Algebra 178 (2003), 49–71. reprint
33. J. G. Pitkethly and B. A. Davey, A non-dualisable entropic algebra, Algebra Universalis 47 (2002), 51–54. reprint
34. D. M. Clark, B. A. Davey and J. G. Pitkethly, Binary homomorphisms and natural dualities, J. Pure Appl. Algebra 169 (2002), 1–28. reprint
35. B. A. Davey and B. J. Knox, From rectangular bands to k-primal algebras, Semigroup Forum 64 (2002), 29–54. preprint
36. B. A. Davey, M. Haviar and H. A. Priestley, Kleene algebras: a case-study of clones and dualities from endomorphisms, Acta Sci. Math. (Szeged) 67 (2001), 77–103. preprint
37. B. A. Davey and J. G. Pitkethly, Dualisability of p-semilattices, Algebra Universalis 45 (2001), 149–153. reprint
38. B. A. Davey and R. Willard, The dualisability of a quasi-variety is independent of the generating algebra, Algebra Universalis 45 (2001), 103–106. reprint
39. B. A. Davey and M. Haviar, A schizophrenic operation which aids the efficient transfer of strong dualities, Houston J. Math. 26 (2000), 215–222. preprint
40. B. A. Davey, P. M. Idziak, W. A. Lampe and G. F. McNulty, Dualizability and graph algebras, Discrete Math. 214 (2000), 145–172. reprint
41. B. A. Davey and B. J. Knox, Regularising natural dualities, Acta Math. Univ. Comenian. (N.S.) 68 (1999), 295–318. reprint
42. B. A. Davey and J. G. Pitkethly, Endoprimal algebras, Algebra Universalis 38 (1997), 266–288. reprint
43. B. A. Davey and R. W. Quackenbush, Natural dualities for dihedral varieties, J. Austral. Math. Soc. Ser. A 61 (1996), 216–228.
44. D. M. Clark and B. A. Davey, When is a natural duality “good”?, Algebra Universalis 35 (1996), 265–295. reprint
45. B. A. Davey and H. A. Priestley, Optimal natural dualities for varieties of Heyting algebras, Studia Logica 56 (1996), 67–96. preprint
46. B. A. Davey and H. A. Priestley, Optimal natural dualities II: general theory, Trans. Amer. Math. Soc. 348 (1996), 3673–3711. reprint
47. B. A. Davey, M. Haviar and H. A. Priestley, The syntax and semantics of entailment in duality theory, J. Symbolic Logic 60 (1995), 1087–1114. reprint
48. B. A. Davey, M. Haviar and H. A. Priestley, Endoprimal distributive lattices are endodualisable, Algebra Universalis 34 (1995), 444–453. reprint
49. D. M. Clark and B. A. Davey, The quest for strong dualities, J. Austral. Math. Soc. Ser. A 58 (1995), 248–280. reprint
50. B. A. Davey, L. Heindorf and R. McKenzie, Near unanimity: an obstacle to general duality theory, Algebra Universalis 33 (1995), 428–439. reprint
51. B. A. Davey, R. McKenzie, J. B. Nation and P. P. Pálfy, Braids and their monotone clones, Algebra Universalis 32 (1994), 153–176. reprint
52. B. A. Davey and H. A. Priestley, Partition-induced natural dualities for varieties of pseudo-complemented distributive lattices, Discrete Math. 113 (1993), 41–58. reprint
53. B. A. Davey and H. A. Priestley, Optimal natural dualities, Trans. Amer. Math. Soc. 338 (1993), 655–677. reprint
54. B. A. Davey, V. J. Schumann and H. Werner, From the subalgebras of the square to the discriminator, Algebra Universalis 28 (1991), 500–519. reprint
55. B. A. Davey, R. W. Quackenbush and D. Schweigert, Monotone clones and the varieties they determine, Order 7 (1990), 145–167.
56. B. A. Davey, Monotone clones and congruence modularity, Order 6 (1990), 389–400.
57. B. A. Davey, K. R. Miles and V. J. Schumann, Quasi-identities, Mal'cev conditions and congruence regularity, Acta Sci. Math. (Szeged) 51 (1987), 39–55.
58. C. Ratanaprasert and B. A. Davey, Semimodular lattices with isomorphic graphs, Order 4 (1987), 1–13.
59. B. A. Davey and H. A. Priestley, Generalised piggyback dualities and applications to Ockham algebras, Houston J. Math. 13 (1987), 151–198. reprint
60. B. A. Davey and J. Nieminen, Annihilators in modular lattices, Algebra Universalis 22 (1986), 154–158. reprint
61. B. A. Davey and L. G. Kovács, Absolute subretracts and weak injectives in congruence modular varieties, Trans. Amer. Math. Soc. 297 (1986), 181–196. reprint
62. B. A. Davey and H. A. Priestley, Lattices of homomorphisms, J. Austral. Math. Soc. Ser. A 40 (1986), 364–406.
63. B. A. Davey and G. Davis, Tensor products and entropic varieties, Algebra Universalis 21 (1985), 68–88. reprint
64. B. A. Davey and H. Werner, Piggyback-Dualitäten, Bull. Austral. Math. Soc. 32 (1985), 1–32. [German]
65. B. A. Davey, Dualities for Stone algebras, double Stone algebras, and relative Stone algebras, Colloq. Math. 46 (1982), 1–14.
66. B. A. Davey and I. Rival, Exponents of lattice-ordered algebras, Algebra Universalis 14 (1982), 87–98.
67. B. A. Davey and M. J. McCarthy, A representation theory for the variety generated by the triangle, Acta Math. Acad. Sci. Hungar. 38 (1981), 241–255.
68. B. A. Davey and H. Werner, Distributivity of coproducts over products, Algebra Universalis 12 (1981), 387–394.
69. B. A. Davey and M. S. Goldberg, The free p-algebra generated by a distributive lattice, Algebra Universalis 11 (1980), 90–100.
70. B. A. Davey, On the lattice of subvarieties, Houston J. Math. 5 (1979), 183–192. reprint
71. B. A. Davey and H. Werner, Injectivity and Boolean powers, Math. Z. 166 (1979), 205–223. reprint
72. B. A. Davey, D. Duffus, R. W. Quackenbush and I. Rival, Exponents of finite simple lattices, J. London Math. Soc. (2) 17 (1978), 203–221.
73. B. A. Davey, Subdirectly irreducible distributive double p-algebras, Algebra Universalis 8 (1978), 73–88.
74. B. A. Davey, Weak injectivity and congruence extension in congruence-distributive equational classes, Canad. J. Math. 29 (1977), 449–459.
75. B. A. Davey and B. Sands, An application of Whitman’s condition to lattices with no infinite chains, Algebra Universalis 7 (1977), 171–178.
76. B. A. Davey, Dualities for equational classes of Brouwerian algebras and Heyting algebras, Trans. Amer. Math. Soc. 221 (1976), 119–146. reprint
77. B. A. Davey and I. Rival, Finite sublattices of three-generated lattices, J. Austral. Math. Soc. Ser. A 21 (1976), 171–178.
78. B. A. Davey, W. Poguntke and I. Rival, A characterization of semi-distributivity, Algebra Universalis 5 (1975), 72–75.
79. B. A. Davey, Free products of bounded distributive lattices, Algebra Universalis 4 (1974), 106–107.
80. B. A. Davey, Some annihilator conditions on distributive lattices, Algebra Universalis 4 (1974), 316–322.
81. B. A. Davey, A note on representable posets, Algebra Universalis 3 (1973), 345–347.
82. B. A. Davey, Sheaf spaces and sheaves of universal algebras, Math. Z. 134 (1973), 275–290.
83. B. A. Davey, m-Stone lattices, Canad. J. Math. 24 (1972), 1027–1032.

Articles: Mathematics Education

84. B. A. Davey, Formal concept analysis: its role in teaching lattice theory, Concept Lattices (P. Eklund, ed.), Lecture Notes in Artificial Intelligence 2961, Springer, 2004, pp. 55–56.
85. B. A. Davey, LOGO for little kids, Maths Counts—Who Cares? (Melbourne, 1989) (D. Firth, ed.), Mathematics Association of Victoria, 1989, pp. 219–221.
86. B. A. Davey, You’re a mathematician! Oh! I never was much good at maths, Function 12 (1988), 41–49.
87. B. A. Davey, Logical or illogical? In defence of mathematics, The Age Monthly Review (November, 1983), 5–6.
88. B. A. Davey, Mathematics in the making: inductive reasoning and proofs by induction, Learning and Applying Mathematics (Melbourne, 1978) (E. Williams, ed.), Australian Association of Mathematics Teachers, 1978, pp. 321–324.
89. B. A. Davey, The four-colour theorem, Vinculum 14 (1977), 145–151.

Journal Articles: Childbirth Education

90. B. A. Davey and J. Lumley, Do hospitals with family-centred maternity care policies have lower intervention rates?, Birth 14 (1987), 132–134.
91. B. A. Davey, A survey of Melbourne’s maternity units, The Childbirth Educator 15 (1985), 10–14.
92. B. A. Davey, A survey of Melbourne’s maternity units, Interaction 2 (1984), 8–10.

Reviews: Educational Software

93. B. A. Davey, Email for maths, Your Computer 51 (1990).
94. B. A. Davey, Amy's First Primer and Word Processor for Kids, Your Computer (June, 1988), 62–64.
95. B. A. Davey, Fingerpaint, Your Computer (April, 1988), 65–68.
96. B. A. Davey, KIDGAMES for pre-schoolers, Your Computer (February, 1988), 88–90.
97. B. A. Davey, Music and education, Your Computer (September, 1987), 38–39.
98. B. A. Davey, The Word is out!, Your Computer (September, 1987), 24–25.
99. B. A. Davey, LogoWriter, Your Computer (August, 1987), 26–30.