Bjarni Jónsson Publications

  1. (with A. Tarski) Direct decompositions of finite algebraic systems, Notre Dame Mathematics Lectures, 5 (1947), 64 pp.

     

  2. (with A. Tarski) Cardinal products of isomorphism types, an appendix to A. Tarski, Cardinal Algebras, New York (1949), 253-312.

     

  3. (with H. Federer) Some properties of free groups, Trans. Amer. Math. Soc. 68 (1951), 1-27.

     

  4. A Boolean algebra without proper automorphism, Proc. Amer. Math. Soc. 2 (1951), 766-770.

     

  5. (with A. Tarski) Boolean algebras with operators, Part I, Amer. J. of Math. 73 (1951), 891-939, Part II, ibid, 74 (1952), 127-162.

     

  6. On the representation of lattices, Math. Scand. 1 (1953), 193-206.

     

  7. Modular lattices and Desargues' theorem, Math. Scand. 2 (1954), 295-314.

     

  8. Distributive sublattices of a modular lattice, Proc. Amer. Math. Soc. 6 (1955), 682-688.

     

  9. A unique decompositon theorem for relational addition, an appendix to A. Tarski, Ordinal Algebras, Amsterdam (1956), 99-123.

     

  10. Universal relational systems, Math. Scand. 4 (1956), 193-208.

     

  11. On isomorphism types of groups and other algebraic systems, Math. Scand. 5 (1957), 224-229.

     

  12. On direct decompositions of torsion-free Abelian groups, Math. Scand. 5 (1957), 230-235.

     

  13. Representations of modular lattices and relation algebras, Trans. Amer. Math. Soc. 92 (1959), 449-464.

     

  14. Arguesian lattices of dimension n < 4, Math. Scand. 7 (1959), 131-145.

     

  15. Lattice-theoretic approach to projective and affine geometry, The Axiomatic Method with Special Reference to Geometry and Physics, Amsterdam (1959), 188-203.

     

  16. On direct decompositions of torsion-free Abelian groups, Math. Scand. 7 (1959), 361-371.

     

  17. Representations of complemented modular lattices, Trans. Amer. Math. Soc. 97 (1960), 64-97.

     

  18. Homogeneous universal relational systems, Math. Scand. 8 (1960), 137-142.

     

  19. Extensions of von Neumann's coordinatization theorem, Proc. of Symposia in Pure Mathematics, 2 (1961), Lattice Theory, 65-70.

     

  20. Sublattices of a free lattice, Can. J. of Math. 13 (1961), 256-264.

     

  21. (with F. Galvin) Distributive sublattices of a free lattice, Can. J. of Math. 13 (1961), 265-272.

     

  22. (with A. Tarski) On two properties of free algebras, Math. Scand. 9 (1961), 95-101.

     

  23. Defining relations for full semigroups of finite transformations, Michigan J. of Math. 9 (1962), 77-85.

     

  24. Representations of relatively complemented modular lattices, Trans. Amer. Math. Soc. 103 (1962), 272-303.

     

  25. (with J. Kiefer) Finite sublattice of free lattices, Can. J. of Math. 14 (1962), 487-497.

     

  26. Arithmetic properties of freely alpha-generated lattices, Can. J. of Math. 14 (1962), 476-481.

     

  27. Algebraic extensions of relational systems, Math. Scand. 11 (1962), 179-205.

     

  28. (with P. Crawley) Direct decomposions of algebraic systems, Bull. Amer. Math. Soc. 69 (1963), 541-547.

     

  29. (with P. Crawley) Refinements for infinite direct decompositions of algebraic systems, Pacific J. of Math 14 (1964), 797-855.i

     

  30. (with C. C. Chang and A. Tarski) Refinitement properties for relational structures, Fund. Math. 55 (1964), 249-281.

     

  31. Extensions of relational structures, The Theory of Models, Amsterdam, (1965) 146-157.

     

  32. The unique factorization problem for finite relational structures, Coll. Math. 14 (1966), 1-32.

     

  33. Algebras whose congruence lattices are distributive, Math. Scand. 21 (1967), 110-121.

     

  34. Equational classes of lattices, Math. Scand. 22 (1969), 187-196.

     

  35. Algebras with a prescribed automorphism group, Coll. Math. 19 (1969), 1-4.

     

  36. (with P. Olin) Almost direct products and saturation, Logic and Foundations of Mathematics (Vol. 20 of Compositio Mathematica) (1968), 125-132.

     

  37. On the residuation in the lattice of group varieties, Scientia Islandica (1968) 14-15.

     

  38. (with G. S. Monk) Representation of primary Arguesian lattices, Pacific J. of Math. 30 (1969), 95-139.

     

  39. Relatively free lattices, Coll. Math. 21 (1970), 191-196.

     

  40. Topics in Universal Algebra, Lecture Notes in Mathematics, 250 Springer-Verlag, (1972).

     

  41. Relatively free products of lattices, Algebra Universalis 1 (1972), 362-373.

     

  42. The class of Arguesian lattices is self-dual, Algebra Universalis 2 (1972), 396.

     

  43. Some recent trends in general algebra, Proceedings of the Tarski Symposium, 1971, Proceedings of Symposia in Pure and Appl. Math. 25 (1972), 1-20.

     

  44. (with G. Grätzer and H. Lakser) The amalgamation property for equational classes of modular lattices, Pacific J. of Math. 45 (1973), 507-524.

     

  45. (with T. P. Whaley) Congruence lattices and multiplicity types of algebras, Pacific J. Math. 50 (1974), 505-520.

     

  46. (with Evelyn Nelson) Relatively free products in regular varieties, Algebra Universalis 4 (1974), 14-19.

     

  47. Sums of finitely based lattice varieties, Advances in Mathematics 14 (1974), 454-468.

     

  48. (with G. McNulty and R. Quackenbush) The ascending and descending varietal chains of a variety, Canad. J. Math. 27 (1975), 25-31.

     

  49. Varieties of algebras and their congruence varieties, Proceedings of the 1974 Intermational Congress of Mathematicians, 1 (1975) 315-320.

     

  50. (with P. Olin) Elementary equivalence and relatively free products, Algebra Universalis 6 (1976), 313-326.

     

  51. (with R. Freese) Congruence modularity implies the Arguesian law, Algebra Universalis 6 (1976), 225-228.

     

  52. Identities in congruence varieties, Lattice Theory, Colloq. Math. Soc. János Bolyai, Vol.14, 1976, pp. 195-205.

     

  53. (with J. B. Nation) A report on sublattices of a free lattice, Universal Algebra, Colloq. Math. Soc. János Bolyai, 17 (1977), 223-257.

     

  54. The variety covering the variety of all modular lattices, Math. Scand. 41 (1977), 5-14.

     

  55. (with I. Rival) Critical edges in subdirectly irreducible lattices, Proc. Amer. Math. Soc. 66 (1977), 194-196.

     

  56. (with D. Duffus and I. Rival) Structure results for function lattices, Canad. J. Math. 30 (1978), 392-400.

     

  57. (with I. Rival) Lattice varieties covering the smallest non-modular variety, Pacific J. of Math. 82 (1979), 463-478.

     

  58. On finitely based varieties of algebras. Colloq. Math. 42 (1979), 255-261.

     

  59. Congruence varieties, A modified version of #60, an appendix to G. Gratzer, Universal Algebra, 2nd ed., (1979), 348-377.

     

  60. Congruence varieties, Algebra Universalis 10 (1980), 355-394.

     

  61. Varieties of lattices: Some open problems, Universal Algebra, Colloq. Math. Soc. János Bolyai, 29 (1982), 421-436.

     

  62. (with R. McKenzie) Powers of partially ordered sets: Refinitement and cancellations properties, Math. Scand. 51 (1982), 87-120.

     

  63. Powers of partially ordered sets: The isomorphism group, Math. Scand. 51 (1982), 121-141.

     

  64. The arithmetic of ordered sets, Ordered Sets, Proceedings of the NATO Advanced Study Institute, Banff, Canada, 1981, Reidel Publishing Co., (1982), 3-42.

     

  65. Varieties of relation algebras, Algebra Universalis 15 (1982), 273-299.

     

  66. Maximal algebras of binary relations, Contemporary Mathematics, Amer. Math. Soc., 33 (1984), 299-307.

     

  67. Amalgamation of pure embeddings, Algebra Universalis 19 (1984), 266-268.

     

  68. (with A. Day) The structure of non-Arguesian lattices, Bull. Amer. Math. Soc. 19 (1985), 157-159.

     

  69. Arguesian lattices, Proc. 19th Nordic Congress of Mathematicians, Reykjavik, 1984, (1985), 78-108.

     

  70. (with A. Day) A structural characterization of non-Arguesian lattices, Order 2 (1986), 335-350.

     

  71. The contributions of Alfred Tarski to general algebra, J. Symbolic Logic 51 (1986), 883-889.

     

  72. (with J. B. Nation) Representations of 2-distributive modular lattice of finite length, Acta Sci. Math. 51 (1987), 123-128.

     

  73. (with A. Day) Non-Arguesian configurations in a modular lattice, Acta Sci. Math. 51 (1987) 309-318.

     

  74. Relation algebras and Schröder categories, Discrete Mathematics 70 (1988) 27-45.

     

  75. The theory of binary relations, Colloq. Math. Soc., János Bolyai 54, Algebraic Logic, Budapest, Hungary (1988), 245-292.

     

  76. (with H. Andréka and I. Németi) Relatively free relation algebras, Algebraic Logic and Universal Algebra in Computer Science, Lecture Notes in Mathematics, Springer-Verlag, 425 (1988), 1-14.

     

  77. (with A. Day) Non-Arguesian configurations and gluings of modular lattices, Algebra Universalis 26 (1989), 208-215.

     

  78. Dilworth's work on decompositions in semimodular lattices, The Dilworth Theorems, Selected Papers by Robert P. Dilworth, Birkhauser, (1990) 187-191.

     

  79. Amalgamation in small varieties of lattices, J. Pure, Appl. Algebra 68 (1990), 195-208.

     

  80. (with H. Andréka and 1. Németi) Free algebras in discriminator varieties, Algebra Universalis 28 (1991) 401-447.

     

  81. A survey of Boolean algebras with operators, Algebras and Orders, NATO ASI Series, Kluwer Academic Publishers, (1993) 239-286.

     

  82. (with A. Day, Ch. Herrmann, J.B. Nation and Douglas Pickering) Small non-Arguesian lattices, Algebra Universilis 31 (1994), 66-94.

     

  83. (with C. Tsinakis) Relation algebras as residuated Boolean algebras, Algebra Universalis 30 (1993), 469-478.

     

  84. On the canonicity of Sahlqvist identities, Studia Logica 53 (1994), 473-491.

     

  85. (with M. Gehrke) Bounded distributive lattices with operators, Mathematica Japonica 40 (1994), 207-215.

     

  86. (with P. Jipsen and J. Rafter) Adjoining units to residuated Boolean algebras, Algebra Universalis 34 (1995), 118-127.

     

  87. The preservation theorem for canonical extensions of Boolean algebras with operators, Lattice Theory and its Applications, in celebration of Garrett Birkhoff's 80th Birthday, Research and Expositions in Mathemeitics, (eds K. A. Baker and R. Wille.), Haldermann Verlag, 23 (1995), 121-130.

     

  88. Congruence distributive varieties, Mathematica Japonica 42 (1995), 353-402.

     

  89. (with M. Gehrke) Monotone bounded distributive lattice lattice expansions.  Mathenatica Japonica 52 (2000), 197-213.

     

  90. (with C. Tsinakis)  Products of classes of residuated structures, Studia Logica 77 (2004), 267-292.

     

  91. (with M. Gehrke) Bounded distributive lattice expansions, Mathematica Scandinavica 94 (2004), 13-45.

     

  92. (with W.J. Blok) Equivalence of consequence operations. Studia Logica 83 (2006), no. 1-3, 91–110.