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My collaboration with E. T. Schmidt spanning six decades

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Reviewing the work of E. T. Schmidt.

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The Publications of E. T. Schmidt

  1. Grätzer, G., Schmidt, E.T.: Über die Anordnung von Ringen. Acta Math. Acad. Sci. Hungar. 8, 259–260 (1957)

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  2. Grätzer, G., Schmidt, E.T.: On the Jordan–Dedekind chain condition. Acta Sci. Math. Szeged 18, 52–56 (1957)

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  3. Grätzer, G., Schmidt, E.T.: On a problem of M. H. Stone. Acta Math. Acad. Sci. Hungar. 8, 455–460 (1957)

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  4. Grätzer, G., Schmidt, E.T.: On the lattice of all join-endomorphisms of a lattice. Proc. Am. Math. Soc. 9, 722–726 (1958)

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  5. Grätzer, G., Schmidt, E.T.: On ideal theory for lattices. Acta Sci. Math. Szeged 19, 82–92 (1958)

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  6. Grätzer, G., Schmidt, E.T.: Characterizations of relatively complemented distributive lattices. Publ. Math. Debrecen 5, 275–287 (1958)

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  7. Grätzer, G., Schmidt, E.T.: Two notes on lattice-congruences. Ann. Univ. Sci. Budapest Eötvös. Sect. Math. 1, 83–87 (1958)

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  8. Grätzer, G., Schmidt, E.T.: Ideals and congruence relations in lattices. Acta Math. Acad. Sci. Hungar. 9, 137–175 (1958)

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  9. Grätzer, G., Schmidt, E.T.: On the generalized Boolean algebra generated by a distributive lattice. Indag. Math. 20, 547–553 (1958)

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  10. Grätzer, G., Schmidt, E.T.: On a theorem of Gábor Szász. Magyar Tud. Akad. Mat. Fiz. Oszt. Közl. 9, 255–258 (1959). (Hungarian)

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  11. Schmidt, E.T.: Congruence relations of algebraic structures. Magyar Tud. Akad. Mat. Fiz. Oszt. Közl. 9, 163–174 (1959). (Hungarian)

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  12. Grätzer, G., Schmidt, E.T.: An associativity theorem for alternative rings. Magyar Tud. Akad. Mat. Kutató Int. Közl. 4, 259–264 (1959)

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  13. Grätzer, G., Schmidt, E.T.: Über einfache Körpererweiterungen. Magyar Tud. Akad. Mat. Kutató Int. Közl. 5, 283–285 (1960)

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  14. Grätzer, G., Schmidt, E.T.: On inaccessible and minimal congruence relations. I. Acta Sci. Math. Szeged 21, 337–342 (1960)

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  15. Grätzer, G., Schmidt, E. T.: A note on a special type of fully invariant subgroups of Abelian groups. Ann. Univ. Sci. Budapest Eötvös Sect. Math. 3–4, 85–87 (1960/1961)

  16. Grätzer, G., Schmidt, E.T.: On a problem of L. Fuchs concerning universal subgroups and universal homomorphic images of abelian groups. Nederl. Akad. Wetensch. Proc. Ser. A 64 = Indag. Math. 23, 253–255 (1961)

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  17. Grätzer, G., Schmidt, E.T.: Standard ideals in lattices. Acta Math. Acad. Sci. Hungar. 12, 17–86 (1961)

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  18. Grätzer, G., Schmidt, E.T.: On congruence lattices of lattices. Acta Math. Acad. Sci. Hungar. 13, 179–185 (1962)

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  19. Grätzer, G., Schmidt, E.T.: Characterizations of congruence lattices of abstract algebras. Acta Sci. Math. (Szeged) 24, 34–59 (1963)

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  20. Schmidt, E.T.: Über die Kongruenzverbände der Verbände. Publ. Math. Debrecen 9, 243–256 (1962)

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  21. Schmidt, E.T.: Universale Algebren mit gegebenen Automorphismengruppen und Unteralgebrenverbänden. Acta Sci. Math. (Szeged) 24, 251–254 (1963)

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  22. Schmidt, E.T.: Universale Algebren mit gegebenen Automorphismengruppen und Kongruenzverbänden. Acta Math. Acad. Sci. Hungar 15, 37–45 (1964)

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  23. Schmidt, E.T.: Remark on a paper of M. F. Janowitz. Acta Math. Acad. Sci. Hungar. 16, 435 (1965)

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  24. Schmidt, E.T.: Über endliche Verbände, die in einen endlichen Zerlegungsverband einbettbar sind. Studia Sci. Math. Hungar 1, 427–429 (1966)

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  25. Schmidt, E.T.: On the definition of homomorphism kernels of lattices. Math. Nachr. 33, 25–30 (1967)

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  26. Schmidt, E.T.: Zur Charakterisierung der Kongruenzverbände der Verbände. Mat. ǎsopis Sloven. Akad. Vied 18, 3–20 (1968)

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  27. Schmidt, E.T.: Kongruenzrelationen algebraischer Strukturen. Mathematische Forschungsberichte, XXV VEB Deutscher Verlag der Wissenschaften, Berlin (1969)

  28. Csákány, B., Schmidt, E.T.: Translations of regular algebras. Acta Sci. Math. (Szeged) 31, 157–160 (1970)

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  29. Schmidt, E.T.: Über reguläre Mannigfaltigkeiten. Acta Sci. Math. (Szeged) 31, 197–201 (1970)

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  30. Schmidt, E.T.: Eine Verallgemeinerung des Satzes von Schmidt-Ore. Publ. Math. Debrecen 17(1970), 283–287 (1971)

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  31. Schmidt, E.T.: Unabhängigkeitsrelationen in Halbverbänden. Period. Math. Hungar. 1, 45–53 (1971)

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  32. Schmidt, E.T.: On \(n\)-permutable equational classes. Acta Sci. Math. (Szeged) 33, 29–30 (1972)

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  33. Schmidt, E.T.: Every finite distributive lattice is the congruence lattice of some modular lattice. Algebra Universalis 4, 49–57 (1974)

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  34. Schmidt, E.T.: Über die Kongruenzrelationen der modularen Verbände. Beiträge zur Algebra und Geometrie, 3. Wiss. Beitr. Martin-Luther-Univ. Halle-Wittenberg Reihe M Math. 5, 59–68 (1974)

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  35. Schmidt, E.T.: A remark on lattice varieties defined by partial lattices. Stud. Sci. Math. Hungar. 9, 195–198 (1975)

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  36. Schmidt, E.T.: On the length of the congruence lattice of a lattice. Algebra Universalis 5, 98–100 (1975)

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  37. Schmidt, E.T.: On finitely generated simple modular lattices. Period. Math. Hungar. 6, 213–216 (1975)

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  38. Fried, E., Schmidt, E.T.: Standard sublattices. Algebra Universalis 5, 203–211 (1975)

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  39. Schmidt, E.T.: On the variety generated by all modular lattices of breadth two. Houst. J. Math. 2, 415–418 (1976)

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  40. Schmidt, E.T.: Lattices generated by partial lattices. In: Lattice theory (Proc. Colloq., Szeged, 1974). Colloq. Math. Soc. János Bolyai, vol. 14, pp. 343–353. North-Holland, Amsterdam (1976)

  41. Schmidt, E.T.: Remarks on finitely projected modular lattices. Acta Sci. Math. (Szeged) 41, 187–190 (1979)

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  42. Schmidt, E.T.: Starre Quotienten in modularen Verbänden. In: Contributions to general algebra (Proc. Klagenfurt Conf., Klagenfurt, 1978), pp. 331–339, Heyn, Klagenfurt (1979)

  43. Schmidt, E.T.: Remark on generalized function lattices. Acta Math. Acad. Sci. Hungar. 34, 337–339 (1980)

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  44. Schmidt, E.T.: The ideal lattice of a distributive lattice with 0 is the congruence lattice of a lattice. Acta Sci. Math. (Szeged) 43, 153–168 (1981)

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  45. Schmidt, E.T.: On finitely projected modular lattices. Acta Math. Acad. Sci. Hungar. 38, 45–51 (1981)

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  46. Schmidt, E.T.: Remark on compatible and order-preserving function on lattices. Studia Sci. Math. Hungar. 14, 139–144 (1982)

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  47. Schmidt, E.T.: On splitting modular lattices. In: Universal algebra (Esztergom, 1977), Colloq. Math. Soc. János Bolyai, vol. 29, pp. 697–703. North-Holland, Amsterdam (1982)

  48. Schmidt, E.T.: Remarks on dependence relations in relational database models. Alkalmaz. Mat. Lapok 8, 177–182 (1982) (Hungarian)

  49. Schmidt, E.T.: A survey on congruence lattice representations. Teubner Texts in Mathematics, vol. 42. BSB B. G. Teubner Verlagsgesellschaft, Leipzig (1982)

  50. Schmidt, E.T., Wille, R.: Note on compatible operations of modular lattices. Algebra Universalis 16, 395–397 (1983)

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  51. Schmidt, E.T.: Congruence lattices of complemented modular lattices. Algebra Universalis 18, 386–395 (1984)

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  52. Kaarli, K., Márki, L., Schmidt, E.T.: Affine complete semilattices. Monatsh. Math. 99, 297–309 (1985)

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  53. Czédli, G., Huhn, A.P., Schmidt, E.T.: Weakly independent subsets in lattices. Algebra Universalis 20, 194–196 (1985)

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  54. Fried, E., Hansoul, G.E., Schmidt, E.T., Varlet, J.C.: Perfect distributive lattices. Contributions to general algebra (Vienna, 1984), vol. 3, pp. 125–142. Hölder-Pichler-Tempsky, Vienna (1985)

  55. Schmidt, E.T.: Congruence relations related to a given automorphism group of a Boolean lattice. Ann. Univ. Sci. Budapest Eötvös Sect. Math. 29(1986), 269–272 (1987)

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  56. Schmidt, E.T.: On locally order-polynomially complete modular lattices. Acta Math. Hungar. 49, 481–486 (1987)

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  57. Schmidt, E.T.: Homomorphism of distributive lattices as restriction of congruences. Acta Sci. Math. (Szeged) 51, 209–215 (1987)

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  58. Schmidt, E.T.: On a representation of distributive lattices. Period. Math. Hungar. 19, 25–31 (1988)

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  59. Schmidt, E.T.: Polynomial automorphisms of lattices. In: General algebra 1988 (Krems, 1988), pp. 233–240. North-Holland, Amsterdam (1990)

  60. Schmidt, E.T.: Pasting and semimodular lattices. Algebra Universalis 27, 595–596 (1990)

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  61. Schmidt, E.T.: Cover-preserving embedding. Period. Math. Hungar. 23, 17–25 (1991)

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  62. Freese, R., Grätzer, G., Schmidt, E.T.: On complete congruence lattices of complete modular lattices. Int. J. Algebra Comput. 1, 147–160 (1991)

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  63. Fried, E., Grätzer, G., Schmidt, E.T.: Multipasting of lattices. Algebra Universalis 30, 241–261 (1993)

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  64. Grätzer, G., Schmidt, E.T.: “Complete-simple” distributive lattices. Proc. Am. Math. Soc. 119, 63–69 (1993)

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  65. Grätzer, G., Schmidt, E.T.: On the congruence lattice of a Scott-domain. Algebra Universalis 30, 297–299 (1993)

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  66. Schmidt, E.T.: Congruence lattices of modular lattices. Publ. Math. Debrecen 43, 129–134 (1993)

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  67. Grätzer, G., Schmidt, E.T.: Another construction of complete-simple distributive lattices. Acta Sci. Math. (Szeged) 58, 115–126 (1993)

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  68. Grätzer, G., Johnson, P.M., Schmidt, E.T.: A representation of \(\mathfrak{m}\)-algebraic lattices. Algebra Universalis 32, 1–12 (1994)

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  69. Grätzer, G., Schmidt, E.T.: Congruence lattices of function lattices. Order 11, 211–220 (1994)

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  70. Fried, E., Schmidt, E.T.: Cover-preserving embedding of modular lattices. Period. Math. Hungar. 28, 73–77 (1994)

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  71. Grätzer, G., Lakser, H., Schmidt, E.T.: Congruence lattices of small planar lattices. Proc. Am. Math. Soc. 123, 2619–2623 (1995)

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  72. Grätzer, G., Schmidt, E.T.: Do we need complete-simple distributive lattices? Algebra Universalis 33, 140–141 (1995)

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  73. Grätzer, G., Schmidt, E.T.: A lattice construction and congruence-preserving extensions. Acta Math. Hungar. 66, 275–288 (1995)

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  74. Grätzer, G., Schmidt, E.T.: Complete congruence lattices of complete distributive lattices. J. Algebra 171, 204–229 (1995)

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  75. Grätzer, G., Schmidt, E.T.: Congruence lattices of p-algebras. Algebra Universalis 33, 470–477 (1995)

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  76. Grätzer, G., Lakser, H., Schmidt, E.T.: On a result of Birkhoff. Period. Math. Hungar. 30, 183–188 (1995)

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  77. Grätzer, G., Schmidt, E.T.: The strong independence theorem for automorphism groups and congruence lattices of finite lattices. Beiträge Algebra Geom. 36, 97–108 (1995)

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  78. Schmidt, E.T.: Homomorphisms of distributive lattices as restriction of congruences: the planar case. Studia Sci. Math. Hungar. 30, 283–287 (1995)

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  79. Grätzer, G., Schmidt, E.T.: On isotone functions with the substitution property in distributive lattices. Order 12, 221–231 (1995)

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  80. Grätzer, G., Schmidt, E.T.: Algebraic lattices as congruence lattices. The \(m\)-complete case. In: Lattice theory and its applications (Darmstadt, 1991), Res. Exp. Math., vol. 23, pp. 91–101. Heldermann, Lemgo (1995)

  81. Grätzer, G., Lakser, H., Schmidt, E.T.: Congruence representations of join-homomorphisms of distributive lattices: a short proof. Math. Slovaca 46, 363–369 (1996)

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  82. Grätzer, G., Schmidt, E.T.: Complete congruence lattices of join-infinite distributive lattices. Algebra Universalis 37, 141–143 (1997)

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  83. Grätzer, G., Lakser, H., Schmidt, E.T.: Isotone maps as maps of congruences. I. Abstract maps. Acta Math. Hungar. 75, 105–135 (1997)

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  84. Grätzer, G., Schmidt, E.T., Wang, D.: A short proof of a theorem of Birkhoff. Algebra Universalis 37, 253–255 (1997)

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  85. Grätzer, G., Lakser, H., Schmidt, E.T.: Congruence lattices of finite semimodular lattices. Can. Math. Bull. 41, 290–297 (1998)

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  86. Grätzer, G., Lakser, H., Schmidt, E. T.: Restriction of standard congruences on lattices. In: Contributions to general algebra (Klagenfurt, 1997), vol. 10, pp. 167–175. Heyn, Klagenfurt (1998)

  87. Schmidt, E.T.: On automorphism groups of simple Arguesian lattices. Publ. Math. Debrecen 53, 383–387 (1998)

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  88. Grätzer, G., Schmidt, E.T.: Representations of join-homomorphisms of distributive lattices with doubly 2-distributive lattices. Acta Sci. Math. (Szeged) 64, 373–387 (1998)

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  89. Grätzer, G., Schmidt, E.T.: Congruence-preserving extensions of finite lattices to sectionally complemented lattices. Proc. Am. Math. Soc. 127, 1903–1915 (1999)

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  90. Grätzer, G., Schmidt, E.T.: Sublattices and standard congruences. Algebra Universalis 41, 151–153 (1999)

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  91. Grätzer, G., Schmidt, E.T.: On finite automorphism groups of simple Arguesian lattices. Studia Sci. Math. Hungar. 35, 247–258 (1999)

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  92. Grätzer, G., Schmidt, E.T.: Some combinatorial aspects of congruence lattice representations. ORDAL ’96 (Ottawa, ON). Theor. Comput. Sci. 217, 291–300 (1999)

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  93. Grätzer, G., Lakser, H., Schmidt, E.T.: Congruence representations of join-homomorphisms of finite distributive lattices: size and breadth. J. Austral. Math. Soc. Ser. A 68, 85–103 (2000)

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  94. Grätzer, G., Schmidt, E.T.: Complete congruence representations with 2-distributive modular lattices. Acta Sci. Math. (Szeged) 67, 39–50 (2001)

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  95. Grätzer, G., Schmidt, E.T.: Regular congruence-preserving extensions of lattices. The Viktor Aleksandrovich Gorbunov memorial issue. Algebra Universalis 46, 119–130 (2001)

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  96. Grätzer, G., Schmidt, E.T.: Congruence-preserving extensions of finite lattices to semimodular lattices. Houst. J. Math. 27, 1–9 (2001)

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  97. Grätzer, G., Lakser, H., Schmidt, E.T.: Isotone maps as maps of congruences. II. Concrete maps. Acta Math. Hungar. 92, 233–238 (2001)

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  98. Grätzer, G., Schmidt, E.T., Thomsen, K.: Congruence lattices of uniform lattices. Houst. J. Math. 29, 247–263 (2003)

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  99. Grätzer, G., Schmidt, E.T.: On the independence theorem of related structures for modular (Arguesian) lattices. Studia Sci. Math. Hungar. 40, 1–12 (2003)

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  100. Grätzer, G., Schmidt, E.T.: Representing congruence lattices of lattices with partial unary operations as congruence lattices of lattices. I. Interval equivalence. J. Algebra 269, 136–159 (2003)

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  101. Grätzer, G., Schmidt, E.T.: Finite lattices with isoform congruences. General algebra and ordered sets. Tatra Mt. Math. Publ. 27, 111–124 (2003)

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  102. Grätzer, G., Schmidt, E.T.: Congruence class sizes in finite sectionally complemented lattices. Can. Math. Bull. 47, 191–205 (2004)

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  103. Grätzer, G., Quackenbush, R.W., Schmidt, E.T.: Congruence-preserving extensions of finite lattices to isoform lattices. Acta Sci. Math. (Szeged) 70, 473–494 (2004)

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  104. Grätzer, G., Schmidt, E.T.: Finite lattices and congruences. A survey. Algebra Universalis 52, 241–278 (2004)

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  105. Grätzer, G., Greenberg, M., Schmidt, E.T.: Representing congruence lattices of lattices with partial unary operators as congruence lattices of lattices. II. Interval ordering. J. Algebra 286, 307–324 (2005)

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  106. Czédli, G., Schmidt, E.T.: How to derive finite semimodular lattices from distributive lattices? Acta Math. Hungar. 121, 277–282 (2008)

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  107. Czédli, G., Schmidt, E.T.: Frankl’s conjecture for large semimodular and planar semimodular lattices. Acta Univ. Palack. Olomuc. Fac. Rerum Natur. Math. 47, 47–53 (2008)

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  108. Czédli, G., Hartmann, M., Schmidt, E.T.: CD-independent subsets in distributive lattices. Publ. Math. Debrecen 74, 127–134 (2009)

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  109. Czédli, G., Maróti, M., Schmidt, E.T.: On the scope of averaging for Frankl’s conjecture. Order 26, 31–48 (2009)

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  110. Czédli, G., Schmidt, E.T.: CDW-independent subsets in distributive lattices. Acta Sci. Math. (Szeged) 75, 49–53 (2009)

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  111. Schmidt, E.T.: Semimodular lattices and the Hall–Dilworth gluing construction. Acta Math. Hungar. 127, 220–224 (2010)

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  112. Czédli, G., Schmidt, E.T.: A cover-preserving embedding of semimodular lattices into geometric lattices. Adv. Math. 225, 2455–2463 (2010)

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  113. Schmidt, E.T.: Cover-preserving embeddings of finite length semimodular lattices into simple semimodular lattices. Algebra Universalis 64, 101–102 (2010)

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  114. Czédli, G., Schmidt, E.T.: Some results on semimodular lattices. In: Contributions to general algebra, vol. 19, pp. 45–56. Heyn, Klagenfurt (2010)

  115. Czédli, G., Schmidt, E.T.: Finite distributive lattices are congruence lattices of almost-geometric lattices. Algebra Universalis 65, 91–108 (2011)

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  116. Schmidt, E.T.: Congruence lattices and cover-preserving embeddings of finite length semimodular lattices. I. Acta Sci. Math. (Szeged) 77, 47–52 (2011)

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  117. Czédli, G., Schmidt, E.T.: The Jordan–Hölder theorem with uniqueness for groups and semimodular lattices. Algebra Universalis 66, 69–79 (2011)

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  118. Czédli, G., Schmidt, E.T.: Slim semimodular lattices. I. A visual approach. Order 29, 481–497 (2012)

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  119. Czédli, G., Schmidt, E.T.: Slim semimodular lattices. II. A description by patchwork systems. Order 30, 689–721 (2013)

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  120. Czédli, G., Schmidt, E.T.: Composition series in groups and the structure of slim semimodular lattices. Acta Sci. Math. (Szeged) 79, 369–390 (2013)

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  121. Grätzer, G., Schmidt, E.T.: A short proof of the congruence representation theorem of rectangular lattices. Algebra Universalis 71, 65–68 (2014)

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  122. Grätzer, G., Schmidt, E.T.: An extension theorem for planar semimodular lattices. Period. Math. Hungar. 69, 32–40 (2014)

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References

  1. Birkhoff, G.: Lattice Theory. American Mathematical Society Colloquium Publications, vol. 25, revised edn. American Mathematical Society, New York (1948)

  2. Birkhoff, G., Frink, O.: Representation of lattices by sets. Trans. Am. Math. Soc. 64, 299–316 (1948)

    Article  MathSciNet  MATH  Google Scholar 

  3. Czédli, G., Grätzer, G.: Planar Semimodular Lattices: Structure and Diagrams. Chapter 3 in [135] (2014)

  4. Fejes Tóth, L.: Lagerungen in der Ebene, auf der Kugel und im Raum. Die Grundlehren der Mathematischen Wissenschaften, vol. 25. Springer, Berlin (1953)

  5. Grätzer, G.: On the complete congruence lattice of a complete lattice with an application to universal algebra. C. R. Math. Rep. Acad. Sci. Canada 11, 105–108 (1989)

    MathSciNet  MATH  Google Scholar 

  6. Grätzer, G.: The Congruences of a Finite Lattice, A Proof-by-Picture Approach. Birkhäuser, Boston (2006)

    MATH  Google Scholar 

  7. Grätzer, G.: Lattice Theory: Foundation. Birkhäuser, Basel (2011)

    Book  MATH  Google Scholar 

  8. Grätzer, G., Knapp, E.: Notes on planar semimodular lattices. I. Construction. Acta Sci. Math. (Szeged) 73, 445–462 (2007)

    MathSciNet  MATH  Google Scholar 

  9. Grätzer, G., Knapp, E.: A note on planar semimodular lattices. Algebra Universalis 58, 497–499 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  10. Grätzer, G., Knapp, E.: Notes on planar semimodular lattices. II. Congruences. Acta Sci. Math. (Szeged) 74, 37–47 (2008)

    MathSciNet  MATH  Google Scholar 

  11. Grätzer, G., Knapp, E.: Notes on planar semimodular lattices. III. Rectangular lattices. Acta Sci. Math. (Szeged) 75, 29–48 (2009)

    MathSciNet  MATH  Google Scholar 

  12. Grätzer, G., Knapp, E.: Notes on planar semimodular lattices. IV. The size of a minimal congruence lattice representation with rectangular lattices. Acta Sci. Math. (Szeged) 76, 3–26 (2010)

    MathSciNet  MATH  Google Scholar 

  13. Grätzer, G., Wehrung, F. (eds.): Lattice Theory: Special Topics and Applications, vol. 1. Birkhäuser, Basel (2014)

  14. Grätzer, G.: Two Topics Related to Congruence Lattices of Lattices. Chapter 10 in [135] (2014)

  15. Grätzer, G.: Planar Semimodular Lattices: Congruences. Chapter 4 in [135] (2014)

  16. Grätzer, G., Wehrung, F. (eds.): Lattice Theory: Special Topics and Applications, vol. 2. Birkhäuser, Basel (2016)

  17. Grätzer, G.: The Congruences of a Finite Lattice, A Proof-by-Picture Approach, 2nd edn. Birkhäuser, Basel (2016)

    Book  MATH  Google Scholar 

  18. Grätzer, G.: Remembering Ervin Fried and Jiří Sichler. Algebra Universalis 76, 127–138 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  19. Grätzer, G., Lakser, H.: On complete congruence lattices of complete lattices. Trans. Am. Math. Soc. 327, 385–405 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  20. Rédei, L.: Algebra, vol. I. Akadémiai Kiadó, Budapest (1954)

    MATH  Google Scholar 

  21. van der Waerden, B.L.: Algebra. 3te Aufl. Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete, vol. 34. Springer, Berlin (1955)

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  1. Department of Mathematics, University of Manitoba, Winnipeg, MB, R3T 2N2, Canada

    G. Grätzer

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  1. G. Grätzer
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Correspondence to G. Grätzer.

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Presented by R. Quackenbush.

This article is part of the topical collection “In memory of E. Tamás Schmidt” edited by Robert W. Quackenbush.

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Grätzer, G. My collaboration with E. T. Schmidt spanning six decades. Algebra Univers. 79, 1 (2018). https://doi.org/10.1007/s00012-018-0485-0

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