# Bjarni Jónsson’s research publications

1. B. J?nsson, A. Tarski, **Direct decompositions of finite algebraic systems**, *Notre Dame Math. Lectures 5*, v+64 pp, 1947

2. B. J?nsson, A. Tarski, **Cardinal products of isomorphism types**, appendix in Cardinal Algebras, *Oxford University Press*, 1949

3. H. Federer, B. J?nsson, **Some properties of free groups**, *Trans. Amer. Math. Soc.* 68 (1), 1-27, 1950

4. B. J?nsson, **A Boolean algebra without proper automorphisms**, *Proc. Amer. Math. Soc.* 2 (5), 766-770, 1951

5a. B. J?nsson, A. Tarski, **Boolean algebras with operators, Part I**, *American J. Math.* 73 (4), 891-939, 1951

5b. B. J?nsson, A. Tarski, **Boolean algebras with operators, Part II**, *American J. Math.* 74 (1), 127-162, 1952

6. B. J?nsson, **On the representation of lattices**, *Math. Scand. 1,* 193-206, 1954

7. B. J?nsson, **Modular lattices and Desargues’ theorem**, *Math. Scand.* 2, 295-314, 1955

8. B. J?nsson, **Distributive sublattices of a modular lattice**, *Proc. Amer. Math. Soc.* 6 (5), 682-688, 1955

9. B. J?nsson, **A unique decomposition theorem for relational addition**, Appendix B of Tarski’s Ordinal Algebras, 99-125, 1956

10. B. J?nsson, **Universal relational systems**, *Math. Scand.* 4, 193-208, 1957

11. B. J?nsson, **On isomorphism types of groups and other algebraic systems**, *Math. Scand.* 5, 224-229, 1958

12. B. J?nsson, **On direct decompositions of torsionfree abelian groups**, *Math. Scand.* 5, 230-235, 1958

13. B. J?nsson, **Representation of modular lattices and of relation algebras,** *Trans. Amer. Math. Soc.* 92 (3), 449-464, 1959

14. B. J?nsson, **Arguesian lattices of dimension n? 4**, *Math. Scand.* 7, 133-145, 1959

15. B. J?nsson, **Lattice-theoretic approach to projective and affine geometry**, *Stud. in Logic Found. of Math.* 27, 188-203, 1959

16. B. J?nsson, **On direct decomposition of torsion free Abelian groups**, *Math. Scand.* 7, 361-371, 1960

17. B. J?nsson, **Representations of complemented modular lattices**, *Trans. Amer. Math. Soc.* 97 (1), 64-94, 1960

18. B. J?nsson, **Homogeneous universal relational systems**, *Math. Scand.* 8 (1), 137-142, 1960

19. B. J?nsson, **Extensions of von Neumann?s coordinatization theorem**, *Proc. Symp. Pure Math.* 2, 65-70, 1961

20. B. J?nsson, **Sublattices of a free lattice**, *Canad. J. Math.* 13, 256-264, 1961

21. F. Galvin, B. J?nsson, **Distributive sublattices of a free lattice**, *Canad. J. Math.* 13, 265-272, 1961

22. B. J?nsson, A. Tarski, **On two properties of free algebras**, *Math. Scand.* 9 (1a), 95-101, 1961

23. B. J?nsson, **Defining relations for full semigroups of finite transformations**, *The Michigan Math.* J. 9 (1), 77-85, 1962

24. B. J?nsson, **Representations of relatively complemented modular lattices**, *Trans. Amer. Math. Soc.* 103 (2), 272-303, 1962

25. B. J?nsson, J. E. Kiefer, **Finite sublattices of a free lattice**, *Canad. J. Math.* 14, 487-497, 1962

26. B. J?nsson, **Arithmetic properties of freely ?-generated lattices**, *Canad. J. Math.* 14, 476-481, 1962

27. B. J?nsson, **Algebraic extensions of relational systems**, *Math. Scand.* 11 (2), 179-205, 1963

28. P. Crawley, B. J?nsson, **Direct decompositions of algebraic systems**, *Bull. Amer. Math. Soc.* 69 (4), 541-547, 1963

29. P. Crawley, B. J?nsson, **Refinements for infinite direct decompositions of algebraic systems**, *Pacific J. Math.* 14 (3), 797-855, 1964

30. C. C. Chang, B. J?nsson, A. Tarski, **Refinement properties for relational structures**, *Fund. Math.* 55 (3), 249-281, 1964

31. B. J?nsson, **Extensions of relational structures**, *The Theory of Models* (Proc. 1963 Internat. Sympos. Berkeley) North-Holland, Amsterdam, 146-157, 1965

32. B. J?nsson, **The unique factorization problem for finite relational structures**, *Colloq. Math.* 14 (1), 1-32, 1966

33. B. J?nsson, **Algebras whose congruence lattices are distributive**, *Math. Scand.* 21, 110-121, 1968

34. B. J?nsson, **Equational classes of lattices**, *Math. Scand.* 22 (1), 187-196, 1969

35. B. J?nsson, **Algebraic structures with prescribed automorphism groups**, *Colloq. Math.* 19 (1), 1-4, 1968

36. B. J?nsson, P. Olin, **Almost direct products and saturation**, *Compositio Math.* 20, 125-132, 1968

37. B. J?nsson, **On the residuation in the lattice of group varieties**, Scientia Islandica, 14-15, 1968

38. B. J?nsson, G. S. Monk, **Representations of primary Arguesian lattices**, *Pacific J. Math.* 30 (1), 95-139, 1969

39. B. J?nsson, **Relatively free lattices**, *Colloq. Math.* 2 (21), 191-196, 1970

40. B. J?nsson, **The class of Arguesian lattices is self-dual**, *Algebra Universalis* 2 (1), 396-396, 1972

41. B. J?nsson, **Relatively free products of lattices**, *Algebra Universalis* 1 (1), 362-373, 1971

42. B. J?nsson, **Topics in Universal Algebra**, *Lecture Notes in Math.* 250, Springer Verlag, vi+220 pp, 1972

43. G. Gr?tzer, B. J?nsson, H. Lakser, **The amalgamation property in equational classes of modular lattices**, *Pacific J. Math.* 45 (2), 507-524, 1973

44. B. J?nsson, E. Nelson, **Relatively free products in regular varieties**, *Algebra Universalis* 4 (1), 14-19, 1974

45. B. J?nsson, T. Whaley, **Congruence relations and multiplicity types of algebras**, *Pacific J. Math.* 50 (2), 505-520, 1974

46. B. J?nsson, **Some recent trends in general algebra**, Proceedings of the Tarski Symposium at Berkeley 1971, *Proc. Sympos. Pure Math. 25, Amer. Math. Soc.* 1-19, 1974

47. B. J?nsson, **Sums of finitely based lattice varieties**, *Advances in Math.* 14 (4), 454-468, 1974

48. B. J?nsson, G. McNulty, R. Quackenbush, **The ascending and descending varietal chains of a variety**, *Canad. J. Math.* 27, 25-32, 1975

49. B. J?nsson, **Varieties of algebras and their congruence varieties**, *Proc. of the Internat. Congress of Math.* (Vancouver, 1974) 1, 315-320, 1975

50. B. J?nsson, P. Olin, **Elementary equivalence and relatively free products of lattices**, *Algebra Universalis* 6 (1), 313-325, 1976

51. R. Freese, B. J?nsson, **Congruence modularity implies the Arguesian identity**, *Algebra Universalis* 6 (1), 225-228, 1976

52. B. J?nsson, **Identities in congruence varieties**, Lattice theory (Szeged 1974), *Colloq. Math. Soc. J?nos Bolyai* 14, 195-205, 1976

53. B. J?nsson, J. B. Nation, **A report on sublattices of a free lattice**, Contributions to Universal Algebra (Szeged 1975), *Colloq. Math. Soc. J?nos Bolyai* 17, 223-257, 1977

54. B. J?nsson, **The variety covering the variety of all modular lattices**, *Math. Scand.* 41 (1), 5-14, 1978

55. B. J?nsson, I. Rival, **Critical edges in subdirectly irreducible lattices**, *Proc. Amer. Math. Soc.* 66 (2), 194-196, 1977

56. B. J?nsson, I. Rival, **Lattice varieties covering the smallest nonmodular variety**, *Pacific J. Math.* 82 (2), 463-478, 1979

57. B. J?nsson, **On finitely based varieties of algebras**, *Colloq. Math.* 42 (1), 255-261, 1979

58. D. Duffus, B. J?nsson, I. Rival, **Structure results for function lattices**, *Canad. J. Math.* 30 (2), 392-400, 1978

60. B. J?nsson, **Congruence varieties**, *Algebra Universalis* 10 (1), 355-394, 1980

61. B. J?nsson, **Varieties of lattices: Some open problems**, *Colloq. Math. Soc. J?nos Bolyai* 29, 421-436, 1982

62. B. J?nsson, R. McKenzie, **Powers of partially ordered sets: Cancellation and refinement properties**, *Math. Scand.* 51 (1), 87-120, 1982

63. B. J?nsson, **Powers of partially ordered sets: the automorphism group**, Math. Scand. 51 (1), 121-141, 1982

64. B. J?nsson, **Arithmetic of ordered sets**, Ordered sets (Banff 1981),?*NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci.* 83, Reidel, 3-41, 1982

65. B. J?nsson, **Varieties of relation algebras**, *Algebra Universalis* 15 (1), 273-298, 1982

66. B. J?nsson, **Maximal algebras of binary relations**, *Contemp. Math.* 33, 299-307, 1984

67. B. J?nsson, **Amalgamation of pure embeddings**, *Algebra Universalis* 19 (2), 266-268, 1984

68. A.Day, B. J?nsson, **The structure of non-Arguesian lattices**, *Bull. Amer. Math. Soc.* 13 (2), 157-159, 1985

69. B. J?nsson, **Arguesian lattices**, *Proc. 19th Nordic Congress of Mathematicians*, Reykjavik 1985, 78-108, 1984

70. A. Day, B. J?nsson, **A structural characterization of non-Arguesian lattices**, *Order* 2 (4), 335-350, 1985

71. B. J?nsson, **The contributions of Alfred Tarski to general algebra**, *J. Symbolic Logic* 51 (4), 883-889, 1986

72. B. J?nsson, J. B. Nation, **Representation of 2-distributive modular lattices of finite length**, *Acta Sci. Math.* 51 (1-2), 123-128, 1987

73. A. Day, B. J?nsson, **Non-Arguesian configurations in a modular lattice**, *Acta Sci. Math.* 51 (3-4), 309-318, 1987

74. B. J?nsson, **Relation algebras and Schr?der categories**, *Discrete Math.* 70 (1), 27-45, 1988

75. B. J?nsson, **The theory of binary relations**, Algebraic logic (Budapest 1988) *Colloq. Math. Soc. J?nos Bolyai* 54, North-Holland, Amsterdam, 245-292, 1991

76. A. Day, B. J?nsson, **Non-Arguesian configurations and gluings of modular lattices**, *Algebra Universalis* 26 (2), 208-215, 1989

77. H. Andr?ka, B. J?nsson, I. N?meti, **Relatively free relation algebras**, Algebraic Logic and Universal Algebra in Computer Science (Ames, IA, 1988), *Lecture Notes in Comput. Sci.* 425, 1-14, 1990

78. B. J?nsson, **Dilworth?s work on decompositions in semimodular lattices**, The Dilworth Theorems, *Contemp. Math.*, Birkh?user, 187-191, 1990

79. B. J?nsson, **Amalgamation in small varieties of lattices**, *J. Pure Appl. Algebra* 68 (1-2), 195-208, 1990

80. H. Andr?ka, B. J?nsson, I. N?meti, **Free algebras in discriminator varieties**, *Algebra Universalis* 28 (3), 401-447, 1991

81. B. J?nsson, **A survey of Boolean algebras with operators**, Algebras and Orders (Montreal 1991), *NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci.* 389, Kluwer, 239-286, 1993

82. B. J?nsson, C Tsinakis, **Relation algebras as residuated Boolean algebras**, *Algebra Universalis* 30 (4), 469-478, 1993

83. A. Day, C. Herrmann, B. J?nsson, J. B. Nation, D. Pickering, **Small non-Arguesian lattices**, *Algebra Universalis* 31 (1), 66-94, 1994

84. B. J?nsson, **On the canonicity of Sahlqvist identities**, *Studia Logica* 53 (4), 473-491, 1994

85. M. Gehrke, B. J?nsson, **Bounded distributive lattices with operators**, *Math. Japon.* 40 (2), 207-215, 1994

86. P. Jipsen, B. J?nsson, J. Rafter, **Adjoining units to residuated Boolean algebras**, *Algebra Universalis* 34 (1), 118-127, 1995

87. B. J?nsson, **Congruence distributive varieties**, *Math. Japon.* 42 (2), 353-401, 1995

88. B. J?nsson, **The preservation theorem for canonical extensions of Boolean algebras with operators**, Lattice theory and its applications (Darmstadt 1991), *Res. Exp. Math.* 23, Heldermann, 121-130, 1995

89. M. Gehrke, B. J?nsson, **Monotone bounded distributive lattice expansions**, *Math. Japon.* 52 (2), 197-213, 2000

90. M. Gehrke, B. J?nsson, **Bounded distributive lattice expansions**, *Math. Scand.* 94 (1), 13-45, 2004

91. B. J?nsson, C. Tsinakis, **Products of classes of residuated structures**, *Studia Logica* 77 (2), 267-292, 2004

92. W. J. Blok, B. J?nsson, **Equivalence of consequence operations**, *Studia Logica* 83 (1), 91-110, 2006