Article
Full entry |
PDF
(0.3 MB)
Feedback
PDF
(0.3 MB)
Feedback
Keywords:
tolerance simple and tolerance-trivial lattices; locally order-polynomially complete lattices
tolerance simple and tolerance-trivial lattices; locally order-polynomially complete lattices
Summary:
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.
References:
[1] H.-J. Bandelt: Tolerance relations on lattices. Bull. Austral. Math. Soc. 23 (1981), 367–381. DOI 10.1017/S0004972700007255 | MR 0625179 | Zbl 0449.06005
[2] I. Chajda: Algebraic Theory of Tolerance Relations. Univerzita Palackého Olomouc, Olomouc, 1991. Zbl 0747.08001
[3] I. Chajda and J. Nieminen: Direct decomposability of tolerances on lattices, semilattices and quasilattices. Czechoslovak Math. J. 32 (1982), 110–115. MR 0646716
[4] I. Chajda, J. Niederle and B. Zelinka: On existence conditions for compatible tolerances. Czechoslovak Math. J. 26 (1976), 304–311. MR 0401561
[5] P. Crawley: Lattices whose congruences form a Boolean algebra. Pacific J. Math. 10 (1960), 787–795. DOI 10.2140/pjm.1960.10.787 | MR 0113816 | Zbl 0093.03802
[6] R. P. Dilworth: The structure of relatively complemented lattices. Ann. Math. 51 (1950), 348–359. DOI 10.2307/1969328 | MR 0033795 | Zbl 0036.01802
[7] G. Grätzer: General Lattice Theory, Second edition. Birkhäuser-Verlag, Basel-Stuttgart, 1991. MR 1670580
[8] G. Grätzer and E. T. Schmidt: Ideals and congruence relations in lattices. Acta Math. Acad. Sci. Hungar. 9 (1958), 137–175. DOI 10.1007/BF02023870 | MR 0100560
[9] Z. Heleyova: Tolerances on semilattices. Math. Pannon. 9 (1998), 111–119. MR 1620418 | Zbl 0902.06018
[10] K. Kaarli and K. Täht: Strictly locally order affine complete lattices. Order 10 (1993), 261–270. DOI 10.1007/BF01110547 | MR 1267192
[11] T. Katriňák and S. El-Assar: Algebras with Boolean and Stonean congruence lattices. Acta Math. Hungar. 48 (1986), 301–316. DOI 10.1007/BF01951357 | MR 0861848
[12] J. Niederle: A note on tolerance lattices. Čas. pěst. Mat. 107 (1982), 221–224. MR 0673045 | Zbl 0502.08004
[13] S. Radeleczki: A note on the tolerance lattice of atomistic algebraic lattices. Math. Pann. 13 (2002), 183–190. MR 1932424 | Zbl 1006.06004
[14] J. G. Raftery, I. G. Rosenberg and T. Sturm: Tolerance relations and BCK algebras. Math. Japon. 36 (1991), 399–410. MR 1109222
[15] I. G. Rosenberg and D. Schweigert: Compatible orderings and tolerances of lattices. Ann. Discrete Math. 23 (1984), 119–150. MR 0779849
[16] E. T. Schmidt: On locally order-polynomially complete modular lattices. Acta Math. Hungar. 49 (1987), 481–486. DOI 10.1007/BF01951011 | MR 0891060 | Zbl 0646.06008
[17] D. Schweigert: Compatible relations of modular and orthomodular lattices. Proc. Amer. Math. Soc. 81 (1981), 462–464. DOI 10.1090/S0002-9939-1981-0597663-5 | MR 0597663 | Zbl 0458.06005
[18] D. Schweigert: Über endliche ordnungspolynomvollständige Verbände. Monatsh. Math. 78 (1974), 68–76. DOI 10.1007/BF01298196 | MR 0340124 | Zbl 0287.06004
[19] M. Stern: Semimodular Lattices, Theory and Applications. Cambridge University Press, Cambridge-New York-Melbourne, 1999. MR 1695504 | Zbl 0957.06008
[20] G. Szász: Einführung in die Verbändstheorie. Akadémiai Kiadó, Budapest, 1962. MR 0138567
[21] T. Tanaka: Canonical subdirect factorization of lattices. J. Sci. Hiroshima Univ., Ser. A 16 (1952), 239–246. DOI 10.32917/hmj/1557367260 | MR 0060476
Search
Partner of
