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Tribute to Bjarni Jónsson

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Publications of Bjarni Jónsson

  1. (with A. Tarski): Direct decompositions of finite algebraic systems. Notre Dame Mathematics Lectures, no. 5. Notre Dame, Indiana (1947)

  2. (with A. Tarski): Cardinal products of isomorphism types. Appendix to: Tarski, A.: Cardinal Algebras, pp. 253–312. Oxford Univ. Press, New York (1949)

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

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

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  5. (with A. Tarski): Boolean algebras with operators: Part I. Amer. J. of Math. 73, 891–939 (1951)

  6. (with A. Tarski): Boolean algebras with operators, Part II. Amer. J. of Math. 74, 127–162 (1952)

  7. On the representation of lattices: Math. Scand. 1, 193–206 (1953)

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  8. Modular lattices and Desargues’ theorem: Math. Scand. 2, 295–314 (1954)

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

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  10. A unique decomposition theorem for relational addition. Appendix to: Tarski, A.: Ordinal Algebras, pp. 99–123. North-Holland, Amsterdam (1956)

  11. Universal relational systems: Math. Scand. 4, 193–208 (1956)

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

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

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  14. Representations of modular lattices and relation algebras: Trans. Amer. Math. Soc. 92, 449–464 (1959)

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  15. Arguesian lattices of dimension: \(n \le 4\). Math. Scand. 7, 131–145 (1959)

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

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

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  18. Representations of complemented modular lattices: Trans. Amer. Math. Soc. 97, 64–97 (1960)

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  19. Homogeneous universal relational systems: Math. Scand. 8, 137–142 (1960)

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  20. Extensions of von Neumann’s coordinatization theorem. In: Lattice Theory. Proc. of Symposia in Pure Mathematics, vol. 2, pp. 65–70. (1961)

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

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

  23. ( with A. Tarski): On two properties of free algebras. Math. Scand. 9, 95–101 (1961)

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  24. (with H. Federer): Analytic Geometry and Calculus. Ronald Press, New York (1961)

  25. Defining relations for full semigroups of finite transformations: Michigan J. of Math. 9, 77–85 (1962)

  26. Representations of relatively complemented modular lattices: Trans. Amer. Math. Soc. 103, 272–303 (1962)

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

  28. (with J. Kiefer): Finite sublattices of free lattices. Can. J. of Math. 14, 487–497 (1962)

  29. Algebraic extensions of relational systems: Math. Scand. 11, 179–205 (1962)

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  30. (with P. Crawley): Direct decompositions of algebraic systems. Bull. Amer. Math. Soc. 69, 541–547 (1963)

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  31. (with P. Crawley): Refinements for infinite direct decompositions of algebraic systems. Pacific J. of Math. 14, 797–855 (1964)

  32. (with C. C. Chang and A. Tarski): Refinement properties for relational structures. Fund. Math. 55, 249–281 (1964)

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  33. Extensions of relational structures. In: The Theory of Models, pp. 146–157. North-Holland, Amsterdam (1965)

  34. The unique factorization problem for relational structures: Coll. Math. 14, 1–32 (1966)

  35. Algebras whose congruence lattices are distributive: Math. Scand. 21, 110–121 (1967)

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  36. Equational classes of lattices: Math. Scand. 22, 187–196 (1968)

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  37. Algebras with a prescribed automorphism group. Coll. Math. 19, 1–4 (1968)

  38. (with P. Olin): Almost direct products and saturation. Composito Math. 20, 125–132 (1968)

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

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

  41. Relatively free lattices: Coll. Math. 21, 191–196 (1970)

  42. Topics in Universal Algebra. Lecture Notes in Mathematics, no. 250. Springer-Verlag, New York (1972)

  43. Relatively free products of lattices: Algebra Universalis 1, 362–373 (1972)

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

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  45. Some recent trends in general algebra. In: Proceedings of the Tarski Symposium, 1971, Proceedings of Symposia in Pure and Applied Math., vol. 25, pp. 1–20. Amer. Math. Soc., Providence (1972)

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

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

  48. (with E. Nelson): Relatively free products in regular varieties. Algebra Universalis 4, 14–19 (1974)

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  49. Sums of finitely based lattice varieties: Advances in Math. 14, 454–468 (1974)

  50. (with G. McNulty and R. Quackenbush): The ascending and descending varietal chains of a variety. Can. J. of Math. 27, 25–31 (1975)

  51. Varieties of algebras and their congruence varieties. In: Proceedings of the 1974 International Congress of Mathematicians, vol. 1, pp. 315–320. (1975)

  52. (with R. Freese): Congruence modularity implies the Arguesian law. Algebra Universalis 6, 225–228 (1976)

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  53. (with P. Olin): Elementary equivalence and relatively free products. Algebra Universalis 6, 313–326 (1976)

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  54. Identities in congruence varieties. In: Lattice Theory, Colloq. Math. Soc. János Bolyai, vol. 14, pp. 195–205. North-Holland, Amsterdam (1976)

  55. (with J. B. Nation): A report on sublattices of a free lattice. In: Contributions to Universal Algebra, Colloq. Math. Soc. János Bolyai, vol. 17, pp. 223–257. North-Holland, Amsterdam (1977)

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

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

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  58. (with D. Duffus and I. Rival): Structure results for function lattices. Can. J. of Math. 30, 392–400 (1978)

  59. (with I. Rival): Lattice varieties covering the smallest non-modular v. Pacific J. of Math. 82, 463–478 (1979)

  60. On finitely based varieties of algebras: Coll. Math. 42, 255–261 (1979)

  61. Congruence varieties. Algebra Universalis 10, 355–394 (1980)

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  62. Congruence varieties, a modified version of [61]. Appendix to: Grätzer, G: Universal Algebra, 2nd edn., pp. 348–377. Springer, New York (2008)

  63. Varieties of lattices: Some open problems. In: Universal Algebra, Colloq. Math. Soc. János Bolyai, vol. 29, pp. 421–436. North-Holland, Amsterdam (1982)

  64. (with R. McKenzie): Powers of partially ordered sets. Refinement and cancellation properties. Math. Scand. 51, 87–120 (1982)

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  65. Powers of partially ordered sets: The automorphism group. Math. Scand. 51, 121–141 (1982)

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  66. The arithmetic of ordered sets. In: Ordered Sets, Proceedings of the NATO Advanced Study Institute, Banff, Canada, 1981, pp. 3–42. Reidel, Dordrecht (1982)

  67. Varieties of relation algebras: Algebra Universalis 15, 273–298 (1982)

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  68. Maximal algebras of binary relations. In: Contributions to Group Theory, Contemporary Mathematics, vol. 33, pp. 299–307. Amer. Math. Soc., Providence (1984)

  69. Amalgamations of pure embeddings: Algebra Universalis 19, 266–268 (1984)

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

  71. Arguesian lattices. Proc. 19th Nordic Congress of Mathematicians, Reykjavík, 1984, pp. 78–108. (1985)

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

  73. The contributions of Alfred Tarski to general algebra: J. Symbolic Logic 51, 883–889 (1986)

  74. (with J.B. Nation): Representation of 2-distributive modular lattices of finite length. Acta Sci. Math. (Szeged) 51, 123–128 (1987)

  75. (with A. Day): Non-Arguesian configurations and gluings in a modular lattice. Acta Sci. Math. (Szeged) 51, 309–318 (1987)

  76. Relation algebras and Schröder categories: Discrete Mathematics 70, 27–45 (1988)

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  77. (with H. Andréka and I. Némiti): Relatively free relation algebras. In: Algebraic Logic and Universal Algebra in Computer Science, Lecture Notes in Mathematics, vol. 45, pp. 1–15. Springer-Verlag, New York (1988)

  78. The theory of binary relations, In: Algebraic Logic, Colloq. Math. Soc. János Bolyai, vol. 54, pp. 245–292. North-Holland, Amsterdam (1988)

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

  80. Dilworth’s work on decompositions in semimodular lattices. In: The Dilworth Theorems: Selected Papers by Robert P. Dilworth, pp. 187–191. Birkhäuser, Boston (1990)

  81. Amalgamation in small varieties of lattices: J. Pure and Applied Algebra 68, 195–208 (1990)

  82. (with H. Andréka and I. Némiti): Free algebras in discriminator varieties. Algebra Universalis 28, 401–447 (1991)

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

  84. A survey of Boolean algebras with operators. In: Algebras and Orders (Montreal, PQ, 1991), NATO Adv. Sci. Inst. Ser. C, vol. 389, pp. 239–286. Kluwer, Dordrecht (1993)

  85. (with A. Day, Ch. Herrmann, J.B. Nation and D. Pickering): Small non-Arguesian lattices. Algebra Universalis 31, 66–94 (1994)

  86. (with M. Gehrke): Bounded distributive lattices with operators. Math. Japon. 40, 207–215 (1994)

  87. On the canonicity of Sahlqvist identities: Studia Logica 53, 473–491 (1994)

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

  89. Congruence distributive varieties: Math. Japon. 42, 353–401 (1995)

  90. The preservation theorem for canonical extensions of Boolean algebras with operators. In: Lattice Theory and its Applications (Darmstadt, 1991), Res. Exp. Math., vol. 23, pp. 121–130. Heldermann, Lemgo (1995)

  91. (with M. Gehrke): Monotone bounded distributive lattice expansions. Math. Japon. 52, 197–213 (2000)

  92. (with M. Gehrke): Bounded distributive lattice expansions. Math. Scand. 94, 13–45 (2004)

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  93. (with C. Tsinakis): Products of classes of residuated structures. Studia Logica 77, 267–292 (2004)

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  94. (with W. Blok): Equivalence of consequence relations, with a preface by B. Jónsson. Studia Logica 83, 91–110 (2006)

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  1. Department of Mathematics, University of Hawaiì, Honolulu, HI, 96822, USA

    J. B. Nation

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This article is part of the topical collection “In memory of Bjarni Jónsson” edited by J. B. Nation.

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Nation, J.B. Tribute to Bjarni Jónsson. Algebra Univers. 79, 57 (2018). https://doi.org/10.1007/s00012-018-0542-8

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