Publications of Ralph S. Freese

  1. Ralph Freese, Ralph McKenzie, George McNulty, and Walter Taylor, Algebras, Lattices, Varieties, Volumes II and III. See my books page. A revised, online version.

  2. Ralph Freese and Ralph McKenzie, Commutator theory for congruence modular varieties, 2nd edition. A revised, online version.

  3. H. Peter Gumm and Ralph S. Freese, Free-lattice functors weakly preserve epi-pullbacks, Algebra Universalis, (2022)83:20.

  4. Kira Adaricheva and Ralph Freese and J. B. Nation, Notes on join semidistributive lattices, Intern. J. Algebra & Computation, 32, No. 2(2022), 347-356.

  5. Ralph Freese and J. B. Nation, A simple semidistributive lattice, Intern. J. Algebra & Computation, 31, No. 2(2021), 219-224.

  6. William DeMeo and Ralph Freese and Matthew Valeriote, Polynomial-time tests for difference terms in idempotent varieties, Intern. J. Algebra & Computation, 29, No. 6(2019), 927-949.

  7. Ralph Freese and J. B. Nation and Matthew Valeriote, Testing for a Semilattice Term, Order(2018), 41-77.

  8. Ralph Freese and Ralph McKenzie, Maltsev families of varieties closed under join or Maltsev product , Algebra Universalis, 77(2017), 29-50.

  9. R. Freese and J. B. Nation, Free and Finitely Presented Lattice, Extended Version, an extension of Chapter 2 of Lattice Theory: Special Topics and Applications, vol 2. edited by George Gratzer and Friedrich Wehrung, Springer, 2016, 27-58. This version includes a section on the generalized word problem and automorphisms. This extented version is also available from Springer, for free. (The last item in the table of contents.)
  10. Ralph Freese and J. B. Nation, Projective ordinal sums of lattices and isotone sections, Order, 32(2015), 245-254. Doi: 10.1007/s11083-014-9329-5.

  11. Ralph Freese, Equations implying congruence n-permutability and semidistributivity, Algebra Universalis, 70(2013), 347-357. Doi: 10.1007/s00012-013-0256-x.

  12. Ralph Freese and Matthew Valeriote, On the complexity of some Maltsev conditions, Intern. J. Algebra & Computation, 19(2009), 41-77.

  13. Ralph Freese, Computing Congruences Efficiently, Algebra Universalis, 59(2008), 337-343.
  14. Ralph Freese, George McNulty, and J. B. Nation, A modular inherently nonfinitely based lattice, Algebra Universalis, 55(2006), 119-125.
  15. R. Freese, Automated Lattice Drawing, Lecture Notes in Artificial Intelligence, 2961, Springer, Berlin, 2004, 112-127.
  16. R. Freese, J. Hyndman, J. B. Nation, Whaley's Theorem for Finite Lattices, Order, 20(2004), 223-228. MR2064046
  17. D. Clark, B. Davey, R. Freese, M. Jackson, Standard topological algebras and syntactic congruences, Algebra Universalis, 52(2004), 343-376.
  18. R. Freese, J. Jezek, P. Jipsen, P. Markovic, M. Maroti, R. McKenzie, The Variety Generated by Order Algebras, Algebra Universalis, 47(2002), 103-138. MR1916610 (2003f:08003)
  19. Ralph Freese, George McNulty, and J. B. Nation, Inherently nonfinitely based lattices, Annals of Pure and Applied Logic, 115(2002), 175-193. MR1897025 (2003c:06005)
  20. Ralph Freese, Jaroslav Jezek, and J. B. Nation, Lattices with large minimal extensions, Algebra Universalis, 45 (2001), 221-309. MR1810550 (2002e:06008)
  21. Ralph Freese, Algorithms in Finite, Fintely Presented and Free Lattices, preprint, revised 28 July 1999.
  22. Ralph Freese, Free Lattices, Appendix G of General Lattice Theory by G. Gratzer, Birkhauser (1998), 575-591. MR1670580 (2000b:06001)
  23. Ralph Freese, Computing Congruence Lattices of Finite Lattices, Proc. Amer. Math. Soc. , 125 (1997), 3457-3463. MR1451802 (98h:06016)
  24. M. E. Adams, R. Freese, J. B. Nation, and J. Schmid, Maximal Sublattices and Frattini Sublattices of Bounded Lattices, J. Austral. Math. Soc. Ser. A, 63 (1997), 110-127. MR1456593 (98d:06008)
  25. Ralph Freese, A Review of Roland Schmidt's book Subgroup lattices of groups. Bull. Amer. Math. Soc. 33 (1996), no. 4, 487--492.
  26. Ralph Freese, Keith Kearnes, and J. B. Nation, Congruence lattices of congruence semidistributive algebras. Lattice theory and its applications (Darmstadt, 1991), 63--78, Res. Exp. Math., 23, Heldermann, Lemgo, 1995. 06B10 (08B10). MR1366865 (97a:08015)
  27. Ralph Freese, Jaroslav Je\v zek, and J. B. Nation, Free lattices. Mathematical Surveys and Monographs, 42. American Mathematical Society, Providence, RI, 1995. viii+293 pp. ISBN: 0-8218-0389-1 MR 96c:06013 (Reviewer: T. S. Blyth) 06B25 (06-02 06-04 06B20 68Q25). MR1319815 (96c:06013) Both print and electronic versions available at AMS Bookstore

  28. Ralph Freese, New results on free lattices. Lattice theory and its applications (Darmstadt, 1991), 51--61, Res. Exp. Math., 23, Heldermann, Lemgo, 1995. 06B25. MR1366864 (97b:06004)

  29. R. Freese, Alan Day's early work: congruence identities. Algebra Universalis 34 (1995), no. 1, 4--23, 01A70 (06B10 08A30). MR1344951 (97a:01050)
  30. R. Freese, Finitely based modular congruence varieties are distributive. Algebra Universalis 32 (1994), no. 1, 104--114, MR 95h:06006 (Reviewer: Sheila Oates-Williams) 06B20 (06C05 08B15). MR1287018
  31. Ralph Freese, J. Je\v zek, and J. B. Nation, Term rewrite systems for lattice theory. J. Symbolic Comput. 16 (1993), no. 3, 279--288, 68Q42 (03C05 06-04). MR1259675 (95f:68118)
  32. Ralph Freese, Directions in lattice theory. Algebra Universalis 31 (1994), no. 3, 416--429, MR 95e:06016 (Reviewer: E. T. Schmidt) 06B25 (06C05). MR1265353
  33. Ralph Freese, Lectures on free lattices. Algebras and orders (Montreal, PQ, 1991), 199--237, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 389, Kluwer Acad. Publ., Dordrecht, 1993. MR 94m:06010 (Reviewer: Joel Berman) 06B25 (08B20). MR1233792

  34. Ralph Freese, Free and finitely presented lattices. Proceedings of the International Conference on Algebra, Part 3 (Novosibirsk, 1989), 85--97, Contemp. Math., 131, Part 3, Amer. Math. Soc., Providence, RI, 1992. MR 93k:06016 (Reviewer: Joel Berman) 06B25 (06-02 06B20). MR1175874

  35. Ralph Freese, Douglas Pickering, and Michael Roddy, Obituary: R. Alan Day. Order 8 (1991/92), no. 4, 319--324, 01A70. MR1173137 (93f:01019)

  36. R. Freese, G. Grätzer, and E. T. Schmidt, On complete congruence lattices of complete modular lattices. Internat. J. Algebra Comput. 1 (1991), no. 2, 147--160, MR 92k:06009 (Reviewer: George Hutchinson) 06A23 (06B10 06C05). MR1128008

    pdf version.

  37. Alan Day and Ralph Freese, The role of gluing constructions in modular lattice theory. The Dilworth theorems, 251--260, Contemp. Mathematicians, Birkhäuser Boston, Boston, MA, 1990. 06C05 MR1111499

  38. Ralph Freese, Finitely presented lattices: continuity and semidistributivity. Lattices, semigroups, and universal algebra (Lisbon, 1988), 67--70, Plenum, New York, 1990. 06B05. MR1085067 (91j:06010)

  39. Ralph Freese, On the two kinds of probability in algebra. Algebra Universalis 27 (1990), no. 1, 70--79, MR 91b:03059 (Reviewer: M. A. Ta\u \i tslin) 03C13 (08C99). MR1025836
  40. Ralph Freese, Finitely presented lattices: canonical forms and the covering relation. Trans. Amer. Math. Soc. 312 (1989), no. 2, 841--860, MR 90b:06011 (Reviewer: M. E. Adams) 06B25. MR0949899
  41. Ralph Freese and Ralph McKenzie, Commutator theory for congruence modular varieties. London Mathematical Society Lecture Note Series, 125. Cambridge University Press, Cambridge-New York, 1987. iv+227 pp. ISBN: 0-521-34832-3 MR 89c:08006 (Reviewer: Sheila Oates-Williams) 08B10. MR0909290
  42. Ralph Freese, Free lattice algorithms. Order 3 (1987), no. 4, 331--344, MR 88j:06012 (Reviewer: Joel Berman) 06B25 (06-04 08A50 68Q40). MR0891380
  43. Ralph Freese, A decomposition theorem for modular lattices containing an $n$-diamond. Acta Sci. Math. (Szeged) 51 (1987), no. 1-2, 57--71, MR 88i:06012 (Reviewer: Christian Herrmann) 06C05. MR0911558
  44. Ralph Freese, Connected components of the covering relation in free lattices. Universal algebra and lattice theory (Charleston, S.C., 1984), 82--93, Lecture Notes in Math., 1149, Springer, Berlin-New York, 1985. MR 87k:06015 (Reviewer: M. E. Adams) 06B25. MR0823007

  45. Ralph Freese, J. B. Nation, J. Je\v zek, and V. Slavík, Singular covers in free lattices. Order 3 (1986), no. 1, 39--46, MR 87i:06020 (Reviewer: E. T. Schmidt) 06B25. MR0850396
  46. Ralph Freese and J. B. Nation, Covers in free lattices. Trans. Amer. Math. Soc. 288 (1985), no. 1, 1--42, MR 86f:06016 (Reviewer: Joel Berman) 06B25. MR0773044
  47. Ralph Freese, On Jónsson's theorem. Algebra Universalis 18 (1984), no. 1, 70--76, MR 86e:08007 (Reviewer: H. Peter Gumm) 08B10 (06C05). MR0743457
  48. Gábor Czédli and Ralph Freese, On congruence distributivity and modularity. Algebra Universalis 17 (1983), no. 2, 216--219, MR 85e:08011 (Reviewer: H. Peter Gumm) 08B10 (03D40). MR0726275
  49. Ralph Freese, Subdirectly irreducible algebras in modular varieties. Universal algebra and lattice theory (Puebla, 1982), 142--152, Lecture Notes in Math., 1004, Springer, Berlin-New York, 1983. MR 85c:08011 (Reviewer: H. Peter Gumm) 08B10. MR0716179
  50. Ralph Freese, Some order-theoretic questions about free modular lattices. Ordered sets (Banff, Alta., 1981), pp. 355--377, NATO Adv. Study Inst. Ser. C: Math. Phys. Sci., 83, Reidel, Dordrecht-Boston, Mass., 1982. MR 83j:06011 (Reviewer: T. S. Blyth) 06B25 (06C05). MR0661300
  51. Ralph Freese and Ralph McKenzie, Residually small varieties with modular congruence lattices. Trans. Amer. Math. Soc. 264 (1981), no. 2, 419--430, MR 83d:08012a (Reviewer: W. Taylor) 08B10 (06B10). MR0603772
  52. Ralph Freese, Christian Herrmann, and András P. Huhn, On some identities valid in modular congruence varieties. Algebra Universalis 12 (1981), no. 3, 322--334, MR 82m:08007 (Reviewer: George Hutchinson) 08B10. MR0624298
  53. Alan Day and Ralph Freese, A characterization of identities implying congruence modularity. I. Canad. J. Math. 32 (1980), no. 5, 1140--1167, MR 82b:08009 (Reviewer: Joel Berman) 08B10. MR0596102
  54. Ralph Freese, Free modular lattices. Trans. Amer. Math. Soc. 261 (1980), no. 1, 81--91, MR 81k:06010 (Reviewer: F. B. Cannonito) 06C05 (03D40). MR0576864
  55. Ralph Freese, Projective geometries as projective modular lattices. Trans. Amer. Math. Soc. 251 (1979), 329--342, 06C10 (05B25). MR0531987
  56. Ralph Freese, The variety of modular lattices is not generated by its finite members. Trans. Amer. Math. Soc. 255 (1979), 277--300, MR 81g:06003 (Reviewer: K. A. Baker) 06C05 (06C20). MR0542881
  57. Ralph Freese, William A. Lampe, and Walter Taylor, Congruence lattices of algebras of fixed similarity type. I. Pacific J. Math. 82 (1979), no. 1, 59--68, MR 81d:08004 (Reviewer: Joel Berman) 08A30. MR0549832
  58. Ralph Freese and J. B. Nation, Finitely presented lattices. Proc. Amer. Math. Soc. 77 (1979), no. 2, 174--178, MR 81a:06008 (Reviewer: M. E. Adams) 06B25 (03B25 06B05). MR0542080
  59. Ralph Freese and J. B. Nation, Projective lattices. Pacific J. Math. 75 (1978), no. 1, 93--106, MR 80c:06012 (Reviewer: G. Grätzer) 06B25. MR0500031
  60. R. Freese, Some varieties of modular lattices not generated by their finite dimensional members. Contributions to universal algebra (Colloq., József Attila Univ., Szeged, 1975), pp. 133--144, Colloq. Math. Soc. Janos Bolyai, Vol. 17, North-Holland, Amsterdam, 1977. MR 58 #5433 (Reviewer: George Hutchinson) 06A30 (08A15). MR0485608

  61. Ralph Freese and Bjarni Jónsson, Congruence modularity implies the Arguesian identity. Algebra Universalis 6 (1976), no. 2, 225--228, MR 57 #12340 (Reviewer: M. E. Adams) 08A15. MR0472644
  62. Ralph S. Freese, The structure of modular lattices of width four with applications to varieties of lattices. Mem. Amer. Math. Soc. 9 (1977), no. 181, vii+91 pp. MR 56 #197 (Reviewer: G. Bruns) 06A30. MR0441803

  63. Anna Romanowska and Ralph Freese, Subdirectly irreducible modular double $p$-algebras. Houston J. Math. 3 (1977), no. 1, 109--112, MR 55 #7875 (Reviewer: R. Beazer) 06A35. MR0434911

  64. Ralph Freese and J. B. Nation, $3-3$ lattice inclusions imply congruence modularity. Algebra Universalis 7 (1977), no. 2, 191--194, MR 55 #7870 (Reviewer: Ann Miller) 06A30. MR0434906
  65. R. P. Dilworth and Ralph Freese, Generators of lattice varieties. Algebra Universalis 6 (1976), no. 3, 263--267, MR 55 #210 (Reviewer: James B. Nation) 06A20. MR0427175
  66. Ralph Freese, Congruence lattices of finitely generated modular lattices. Proceedings of the Lattice Theory Conference (Ulm, 1975), pp. 62--70, Univ. Ulm, Ulm, 1975. MR 54 #12590 (Reviewer: E. T. Schmidt) 06A30. MR0424631
  67. Ralph Freese, Planar sublattices of ${\rm FM}(4)$. Algebra Universalis 6 (1976), no. 1, 69--72, MR 53 #2778 (Reviewer: George Hutchinson) 06A30. MR0398927
  68. Ralph Freese, Breadth two modular lattices. Proceedings of the University of Houston Lattice Theory Conference (Houston, Tex., 1973), pp. 409--451, Dept. Math., Univ. Houston, Houston, Tex., 1973. MR 53 #2777 (Reviewer: George Hutchinson) 06A30. MR0398926
  69. Ralph Freese, Ideal lattices of lattices. Pacific J. Math. 57 (1975), no. 1, 125--133, MR 51 #7968 (Reviewer: R. P. Dilworth) 06A20. MR0371751
  70. Ralph Freese and Charles R. Johnson, Comments on the discrete matrix model of population dynamics. J. Res. Nat. Bur. Standards Sect. B 78B (1974), 73--78, MR 50 #6549 (Reviewer: N. Keyfitz) 92A15. MR0354067

  71. Ralph Freese, Inequalities for generalized matrix functions based on arbitrary characters. Linear Algebra and Appl. 7 (1973), 337--345, MR 49 #5028 (Reviewer: Charles R. Johnson) 15A15 (20C15). MR0340273. DOI:

  72. Ralph Freese and J. B. Nation, Congruence lattices of semilattices. Pacific J. Math. 49 (1973), 51--58, MR 48 #10916 (Reviewer: E. T. Schmidt) 06A20. MR0332590
  73. Ralph Freese, An application of Dilworth's lattice of maximal antichains. Discrete Math. 7 (1974), 107--109, MR 48 #10910 (Reviewer: Joel Berman) 06A10. MR0332584

  74. Ralph Freese, Varieties generated by modular lattices of width four. Bull. Amer. Math. Soc. 78 1972 447--450, MR 44 #6567 (Reviewer: E. T. Schmidt) 06.40. MR0289376