Geodesic
Lattices with complemented tolerance lattice
Czechoslovak Mathematical Journal, Tome 54 (2004) no. 2, pp. 407-412
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We characterize lattices with a complemented tolerance lattice. As an application of our results we give a characterization of bounded weakly atomic modular lattices with a Boolean tolerance lattice.
We characterize lattices with a complemented tolerance lattice. As an application of our results we give a characterization of bounded weakly atomic modular lattices with a Boolean tolerance lattice.
Classification : 06B05, 06C05, 06C15
Keywords: tolerance simple and tolerance-trivial lattices; locally order-polynomially complete lattices 
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Radeleczki, S.; Schweigert, D. Lattices with complemented tolerance lattice. Czechoslovak Mathematical Journal, Tome 54 (2004) no. 2, pp. 407-412. http://geodesic.mathdoc.fr/item/CMJ_2004_54_2_a12/

[1] H.-J.  Bandelt: Tolerance relations on lattices. Bull. Austral. Math. Soc. 23 (1981), 367–381. | DOI | MR | Zbl

[2] I.  Chajda: Algebraic Theory of Tolerance Relations. Univerzita Palackého Olomouc, Olomouc, 1991. | Zbl

[3] I.  Chajda and J.  Nieminen: Direct decomposability of tolerances on lattices, semilattices and quasilattices. Czechoslovak Math.  J. 32 (1982), 110–115. | MR

[4] I.  Chajda, J.  Niederle and B.  Zelinka: On existence conditions for compatible tolerances. Czechoslovak Math.  J. 26 (1976), 304–311. | MR

[5] P.  Crawley: Lattices whose congruences form a Boolean algebra. Pacific J.  Math. 10 (1960), 787–795. | DOI | MR | Zbl

[6] R. P.  Dilworth: The structure of relatively complemented lattices. Ann. Math. 51 (1950), 348–359. | DOI | MR | Zbl

[7] G.  Grätzer: General Lattice Theory, Second edition. Birkhäuser-Verlag, Basel-Stuttgart, 1991. | MR

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

[9] Z.  Heleyova: Tolerances on semilattices. Math. Pannon. 9 (1998), 111–119. | MR | Zbl

[10] K.  Kaarli and K.  Täht: Strictly locally order affine complete lattices. Order 10 (1993), 261–270. | DOI | MR

[11] T.  Katriňák and S.  El-Assar: Algebras with Boolean and Stonean congruence lattices. Acta Math. Hungar. 48 (1986), 301–316. | DOI | MR

[12] J.  Niederle: A note on tolerance lattices. Čas. pěst. Mat. 107 (1982), 221–224. | MR | Zbl

[13] S.  Radeleczki: A note on the tolerance lattice of atomistic algebraic lattices. Math. Pann. 13 (2002), 183–190. | MR | Zbl

[14] J. G.  Raftery, I. G.  Rosenberg and T.  Sturm: Tolerance relations and BCK algebras. Math. Japon. 36 (1991), 399–410. | MR

[15] I. G.  Rosenberg and D.  Schweigert: Compatible orderings and tolerances of lattices. Ann. Discrete Math. 23 (1984), 119–150. | MR

[16] E. T.  Schmidt: On locally order-polynomially complete modular lattices. Acta Math. Hungar. 49 (1987), 481–486. | DOI | MR | Zbl

[17] D.  Schweigert: Compatible relations of modular and orthomodular lattices. Proc. Amer. Math. Soc. 81 (1981), 462–464. | DOI | MR | Zbl

[18] D.  Schweigert: Über endliche ordnungspolynomvollständige Verbände. Monatsh. Math. 78 (1974), 68–76. | DOI | MR | Zbl

[19] M.  Stern: Semimodular Lattices, Theory and Applications. Cambridge University Press, Cambridge-New York-Melbourne, 1999. | MR | Zbl

[20] G.  Szász: Einführung in die Verbändstheorie. Akadémiai Kiadó, Budapest, 1962. | MR

[21] T.  Tanaka: Canonical subdirect factorization of lattices. J.  Sci. Hiroshima Univ., Ser.  A 16 (1952), 239–246. | DOI | MR