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Proceedings of the American Mathematical Society

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Compatible relations of modular and orthomodular lattices


Author: Dietmar Schweigert
Journal: Proc. Amer. Math. Soc. 81 (1981), 462-464
MSC: Primary 06C05; Secondary 06C15
DOI: https://doi.org/10.1090/S0002-9939-1981-0597663-5
MathSciNet review: 597663
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Abstract: Let $ L$ be a modular lattice of finite length. $ L$ is a projective geometry if and only if $ L$ has only trivial tolerances.


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  • [1] G. Birkhoff, Lattice theory, 3rd ed., Amer. Math. Soc Colloq. Publ., vol. 25, Amer. Math. Soc., Providence, R. I., 1967. MR 0227053 (37:2638)
  • [2] I. Chaida, J. Niederle and B. Zelinka, On existence conditions for compatible tolerances, Czechoslovak Math. J. 26 (1976), 304-311. MR 0401561 (53:5388)
  • [3] G. D. Findlay, Reflexive homomorphic relations, Canad. Math. Bull. 3 (1960), 131-132. MR 0124251 (23:A1565)
  • [4] J. Hashimoto, Congruence relations and congruence classes in lattices, Osaka J. Math. 15 (1963), 71-86. MR 0151409 (27:1394)
  • [5] C. Hermann, $ S$-verklebte Summen von Verbänden, Math. Z. 130 (1973), 255-274. MR 0342449 (49:7195)
  • [6] G. Grätzer, General lattice theory, Stuttgart, 1978.
  • [7] G. Grätzer and E. T. Schmidt, On congruence lattices of lattices, Acta Math. Acad. Sci. Hungar. 13 (1962), 178-185. MR 0139551 (25:2983)
  • [8] M. Kamara and D. Schweigen, Eine Charakterisierung polynomvollständiger Polaritätsverbände, Arch. Math. (Basel) 30 (1978), 661-664. MR 0491379 (58:10637)
  • [9] H. Werner, A Mal'cev condition for admissible relations, Algebra Universalis 3 (1973), 263. MR 0330009 (48:8348)
  • [10] R. Wille, Eine Charakterisierung endlicher, ordnungspolynomvollständiger Verbände, Arch. Math. (Basel) 28 (1977), 557-560. MR 0447062 (56:5377)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1981-0597663-5
Article copyright: © Copyright 1981 American Mathematical Society

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