Global Utilities

La Trobe University
Department of Mathematics and Statistics

Publications by Professor Brian Davey

Books

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

Book Chapters

  1. B. A. Davey and H. A. Priestley, Distributive lattices and duality, General Lattice Theory (G. Grätzer), Second edition, Birkhäuser, 1998, pp. 499–517.
  2. 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.
  3. 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.
  4. 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.
  5. 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.
  6. 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.
  7. 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.
  8. 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.
  9. 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

  1. B. A. Davey, J. G. Pitkethly and R. Willard, The lattice of alter egos (PDF 397KB), submitted, preprint.
  2. B. A. Davey, M. Jackson, M. Maróti and R. N. McKenzie, Principal and syntactic congruences in congruence-distributive and congruence-permutable varieties (PDF 162KB), J. Aust. Math. Soc., to appear, preprint.
  3. D. M. Clark, B. A. Davey, M. Jackson and J. G. Pitkethly, The axiomatizability of topological prevarieties (PDF 443KB), Adv. Math. 218 (2008), 1604–1653, preprint.
  4. B. A. Davey, M. Haviar and H. A. Priestley, Boolean topological distributive lattices and canonical extensions PDF 178KB), Appl. Categ. Structures 15 (2007), 225–241, preprint.
  5. B. A. Davey, M. Jackson, J. Pitkethly and M. R. Talukder, Natural dualities for semilattice-based algebras (PDF 306KB), Algebra Universalis 57 (2007), 463–490, preprint.
  6. D. M. Clark, B. A. Davey and R. Willard, Not every full duality is strong! (PDF 114KB), Algebra Universalis 57 (2007), 375–381, preprint.
  7. B. A. Davey, J. G. Pitkethly and R. Willard, Dualisability versus residual character: a theorem and a counterexample (PDF 320KB), J. Pure Appl. Algebra 210 (2007), 423–435, preprint.
  8. B. A. Davey, M. Haviar and T. Niven, When is a full duality strong? (PDF 264KB), Houston J. Math. 33 (2007), 1–22, preprint.
  9. B. A. Davey, M. Haviar, T. Niven and N. Perkal, Full but not strong dualities at the finite level: extending the realm (PDF 629KB), Algebra Universalis 56 (2007), 37–56, reprint.
  10. B. A. Davey, Natural dualities for structures (PDF 287KB), Acta Univ. M. Belii Ser. Math. 13 (2006), 3–28, preprint.
  11. B. A. Davey, M. Haviar and R. Willard, Structural entailment (PDF 624KB), Algebra Universalis 54 (2005), 397–416, reprint.
  12. B. A. Davey, M. Haviar and R. Willard, Full does not imply strong, does it? (PDF 624KB), Algebra Universalis 54 (2005), 1–22, reprint.
  13. B. A. Davey and M. R. Talukder, Dual categories for endodualisable Heyting algebras: optimization and axiomatization (PDF 365KB), Algebra Universalis 53 (2005), 331–355, reprint.
  14. D. M. Clark, B. A. Davey, R. S. Freese and M. Jackson, Standard topological algebras: syntactic and principal congruences and profiniteness (PDF 396KB), Algebra Universalis 52 (2004), 343–376, reprint.
  15. B. A. Davey and M. Haviar, Applications of Priestley duality in transferring optimal dualities (PDF 397KB), Studia Logica 78 (2004), 213–236, reprint.
  16. D. M. Clark, B. A. Davey, M. Haviar, J. G. Pitkethly and M. R. Talukder, Standard topological quasi-varieties (PDF 385KB), Houston J. Math. 29 (2003), 859–887, reprint.
  17. B. A. Davey and J. C. Galati, A coalgebraic view of Heyting duality (PDF 185KB), Studia Logica 75 (2003), 259–270, reprint.
  18. D. M. Clark, B. A. Davey and J. G. Pitkethly, The complexity of dualisability: three-element unary algebras (PDF 620KB), Internat. J. Algebra Comput. 13 (2003), 361–391, reprint.
  19. B. A. Davey and M. Haviar, Transferring optimal dualities: theory and practice (PDF 303KB), J. Aust. Math. Soc. 74 (2003), 393–420, preprint.
  20. B. A. Davey and M. R. Talukder, Functor category dualities for varieties of Heyting algebras (PDF 227KB), J. Pure Appl. Algebra 178 (2003), 49–71, reprint.
  21. J. G. Pitkethly and B. A. Davey, A non-dualisable entropic algebra (PDF 167KB), Algebra Universalis 47 (2002), 51–54, reprint.
  22. D. M. Clark, B. A. Davey and J. G. Pitkethly, Binary homomorphisms and natural dualities (PDF 246KB), J. Pure Appl. Algebra 169 (2002), 1–28, reprint.
  23. B. A. Davey and B. J. Knox, From rectangular bands to k-primal algebras (PDF 257KB), Semigroup Forum 64 (2002), 29–54, preprint.
  24. B. A. Davey, M. Haviar and H. A. Priestley, Kleene algebras: a case-study of clones and dualities from endomorphisms (PDF 268KB), Acta Sci. Math. (Szeged) 67 (2001), 77–103, preprint.
  25. B. A. Davey and J. G. Pitkethly, Dualisability of p-semilattices (PDF 63KB), Algebra Universalis 45 (2001), 149–153, reprint.
  26. B. A. Davey and R. Willard, The dualisability of a quasi-variety is independent of the generating algebra (PDF 58KB), Algebra Universalis 45 (2001), 103–106, reprint.
  27. B. A. Davey and M. Haviar, A schizophrenic operation which aids the efficient transfer of strong dualities (PDF 251KB), Houston J. Math. 26 (2000), 215–222, preprint.
  28. B. A. Davey, P. M. Idziak, W. A. Lampe and G. F. McNulty, Dualizability and graph algebras (PDF 215KB), Discrete Math. 214 (2000), 145–172, reprint.
  29. B. A. Davey and B. J. Knox, Regularising natural dualities (PDF 299KB), Acta Math. Univ. Comenian. (N.S.) 68 (1999), 295–318, reprint.
  30. B. A. Davey and J. G. Pitkethly, Endoprimal algebras (PDF 279KB), Algebra Universalis 38 (1997), 266–288, reprint.
  31. B. A. Davey and R. W. Quackenbush, Natural dualities for dihedral varieties, J. Austral. Math. Soc. Ser. A 61 (1996), 216–228.
  32. D. M. Clark and B. A. Davey, When is a natural duality “good”? (PDF 994KB), Algebra Universalis 35 (1996), 265–295, reprint.
  33. B. A. Davey and H. A. Priestley, Optimal natural dualities for varieties of Heyting algebras (PDF 284KB), Studia Logica 56 (1996), 67–96, preprint.
  34. B. A. Davey and H. A. Priestley, Optimal natural dualities II: general theory (PDF 665KB), Trans. Amer. Math. Soc. 348 (1996), 3673–3711, reprint.
  35. B. A. Davey, M. Haviar and H. A. Priestley, The syntax and semantics of entailment in duality theory (PDF 770KB), J. Symbolic Logic 60 (1995), 1087–1114, reprint.
  36. B. A. Davey, M. Haviar and H. A. Priestley, Endoprimal distributive lattices are endodualisable (PDF 576KB), Algebra Universalis 34 (1995), 444–453, reprint.
  37. D. M. Clark and B. A. Davey, The quest for strong dualities (PDF 797KB), J. Austral. Math. Soc. Ser. A 58 (1995), 248–280, reprint.
  38. B. A. Davey, L. Heindorf and R. McKenzie, Near unanimity: an obstacle to general duality theory (PDF 657KB), Algebra Universalis 33 (1995), 428–439, reprint.
  39. B. A. Davey, R. McKenzie, J. B. Nation and P. P. Pálfy, Braids and their monotone clones (PDF 358KB), Algebra Universalis 32 (1994), 153–176, reprint.
  40. B. A. Davey and H. A. Priestley, Partition-induced natural dualities for varieties of pseudo-complemented distributive lattices (PDF 276KB), Discrete Math. 113 (1993), 41–58, reprint.
  41. B. A. Davey and H. A. Priestley, Optimal natural dualities (PDF 614KB), Trans. Amer. Math. Soc. 338 (1993), 655–677, reprint.
  42. B. A. Davey, V. J. Schumann and H. Werner, From the subalgebras of the square to the discriminator (PDF 881KB), Algebra Universalis 28 (1991), 500–519, reprint.
  43. B. A. Davey, R. W. Quackenbush and D. Schweigert, Monotone clones and the varieties they determine, Order 7 (1990), 145–167.
  44. B. A. Davey, Monotone clones and congruence modularity, Order 6 (1990), 389–400.
  45. 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.
  46. C. Ratanaprasert and B. A. Davey, Semimodular lattices with isomorphic graphs, Order 4 (1987), 1–13.
  47. B. A. Davey and H. A. Priestley, Generalised piggyback dualities and applications to Ockham algebras (PDF 617KB), Houston J. Math. 13 (1987), 151–198, reprint.
  48. B. A. Davey and J. Nieminen, Annihilators in modular lattices (PDF 228KB), Algebra Universalis 22 (1986), 154–158, reprint.
  49. B. A. Davey and L. G. Kovács, Absolute subretracts and weak injectives in congruence modular varieties (PDF 417KB), Trans. Amer. Math. Soc. 297 (1986), 181–196, reprint.
  50. B. A. Davey and H. A. Priestley, Lattices of homomorphisms, J. Austral. Math. Soc. Ser. A 40 (1986), 364–406.
  51. B. A. Davey and G. Davis, Tensor products and entropic varieties (PDF 994KB), Algebra Universalis 21 (1985), 68–88, reprint.
  52. B. A. Davey and H. Werner, Piggyback-Dualitäten, Bull. Austral. Math. Soc. 32 (1985), 1–32. [German]
  53. B. A. Davey, Dualities for Stone algebras, double Stone algebras, and relative Stone algebras, Colloq. Math. 46 (1982), 1–14.
  54. B. A. Davey and I. Rival, Exponents of lattice-ordered algebras, Algebra Universalis 14 (1982), 87–98.
  55. 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.
  56. B. A. Davey and H. Werner, Distributivity of coproducts over products, Algebra Universalis 12 (1981), 387–394.
  57. B. A. Davey and M. S. Goldberg, The free p-algebra generated by a distributive lattice, Algebra Universalis 11 (1980), 90–100.
  58. B. A. Davey, On the lattice of subvarieties (PDF 514KB), Houston J. Math. 5 (1979), 183–192, reprint.
  59. B. A. Davey and H. Werner, Injectivity and Boolean powers (PDF 321KB), Math. Z. 166 (1979), 205–223, reprint
  60. 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.
  61. B. A. Davey, Subdirectly irreducible distributive double p-algebras, Algebra Universalis 8 (1978), 73–88.
  62. B. A. Davey, Weak injectivity and congruence extension in congruence-distributive equational classes, Canad. J. Math. 29 (1977), 449–459.
  63. B. A. Davey and B. Sands, An application of Whitman’s condition to lattices with no infinite chains, Algebra Universalis 7 (1977), 171–178.
  64. B. A. Davey, Dualities for equational classes of Brouwerian algebras and Heyting algebras (PDF 616KB), Trans. Amer. Math. Soc. 221 (1976), 119–146, reprint.
  65. B. A. Davey and I. Rival, Finite sublattices of three-generated lattices, J. Austral. Math. Soc. Ser. A 21 (1976), 171–178.
  66. B. A. Davey, W. Poguntke and I. Rival, A characterization of semi-distributivity, Algebra Universalis 5 (1975), 72–75.
  67. B. A. Davey, Free products of bounded distributive lattices, Algebra Universalis 4 (1974), 106–107.
  68. B. A. Davey, Some annihilator conditions on distributive lattices, Algebra Universalis 4 (1974), 316–322.
  69. B. A. Davey, A note on representable posets, Algebra Universalis 3 (1973), 345–347.
  70. B. A. Davey, Sheaf spaces and sheaves of universal algebras, Math. Z. 134 (1973), 275–290.
  71. B. A. Davey, m-Stone lattices, Canad. J. Math. 24 (1972), 1027–1032.

Articles: Mathematics Education

  1. 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.
  2. B. A. Davey, LOGO for little kids, Maths Counts—Who Cares? (Melbourne, 1989) (D. Firth, ed.), Mathematics Association of Victoria, 1989, pp. 219–221.
  3. B. A. Davey, You’re a mathematician! Oh! I never was much good at maths, Function 12 (1988), 41–49.
  4. B. A. Davey, Logical or illogical? In defence of mathematics, The Age Monthly Review (November, 1983), 5–6.
  5. 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.
  6. B. A. Davey, The four-colour theorem, Vinculum 14 (1977), 145–151.

Journal Articles: Childbirth Education

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

Reviews: Educational Software

  1. B. A. Davey, Email for maths, Your Computer 51 (1990).
  2. B. A. Davey, Amy's First Primer and Word Processor for Kids, Your Computer (June, 1988), 62–64.
  3. B. A. Davey, Fingerpaint, Your Computer (April, 1988), 65–68.
  4. B. A. Davey, KIDGAMES for pre-schoolers, Your Computer (February, 1988), 88–90.
  5. B. A. Davey, Music and education, Your Computer (September, 1987), 38–39.
  6. B. A. Davey, The Word is out!, Your Computer (September, 1987), 24–25.
  7. B. A. Davey, LogoWriter, Your Computer (August, 1987), 26–30.

 

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