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Title: Lattices with complemented tolerance lattice (English)
Author: Radeleczki, S.
Author: Schweigert, D.
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 54
Issue: 2
Year: 2004
Pages: 407-412
Summary lang: English
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Category: math
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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. (English)
Keyword: tolerance simple and tolerance-trivial lattices
Keyword: locally order-polynomially complete lattices
MSC: 06B05
MSC: 06C05
MSC: 06C15
idZBL: Zbl 1080.06006
idMR: MR2059261
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Date available: 2009-09-24T11:13:50Z
Last updated: 2020-07-03
Stable URL: http://hdl.handle.net/10338.dmlcz/127898
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Reference: [1] H.-J.  Bandelt: Tolerance relations on lattices.Bull. Austral. Math. Soc. 23 (1981), 367–381. Zbl 0449.06005, MR 0625179, 10.1017/S0004972700007255
Reference: [2] I.  Chajda: Algebraic Theory of Tolerance Relations.Univerzita Palackého Olomouc, Olomouc, 1991. Zbl 0747.08001
Reference: [3] I.  Chajda and J.  Nieminen: Direct decomposability of tolerances on lattices, semilattices and quasilattices.Czechoslovak Math.  J. 32 (1982), 110–115. MR 0646716
Reference: [4] I.  Chajda, J.  Niederle and B.  Zelinka: On existence conditions for compatible tolerances.Czechoslovak Math.  J. 26 (1976), 304–311. MR 0401561
Reference: [5] P.  Crawley: Lattices whose congruences form a Boolean algebra.Pacific J.  Math. 10 (1960), 787–795. Zbl 0093.03802, MR 0113816, 10.2140/pjm.1960.10.787
Reference: [6] R. P.  Dilworth: The structure of relatively complemented lattices.Ann. Math. 51 (1950), 348–359. Zbl 0036.01802, MR 0033795, 10.2307/1969328
Reference: [7] G.  Grätzer: General Lattice Theory, Second edition.Birkhäuser-Verlag, Basel-Stuttgart, 1991. MR 1670580
Reference: [8] G.  Grätzer and E. T.  Schmidt: Ideals and congruence relations in lattices.Acta Math. Acad. Sci. Hungar. 9 (1958), 137–175. MR 0100560, 10.1007/BF02023870
Reference: [9] Z.  Heleyova: Tolerances on semilattices.Math. Pannon. 9 (1998), 111–119. Zbl 0902.06018, MR 1620418
Reference: [10] K.  Kaarli and K.  Täht: Strictly locally order affine complete lattices.Order 10 (1993), 261–270. MR 1267192, 10.1007/BF01110547
Reference: [11] T.  Katriňák and S.  El-Assar: Algebras with Boolean and Stonean congruence lattices.Acta Math. Hungar. 48 (1986), 301–316. MR 0861848, 10.1007/BF01951357
Reference: [12] J.  Niederle: A note on tolerance lattices.Čas. pěst. Mat. 107 (1982), 221–224. Zbl 0502.08004, MR 0673045
Reference: [13] S.  Radeleczki: A note on the tolerance lattice of atomistic algebraic lattices.Math. Pann. 13 (2002), 183–190. Zbl 1006.06004, MR 1932424
Reference: [14] J. G.  Raftery, I. G.  Rosenberg and T.  Sturm: Tolerance relations and BCK algebras.Math. Japon. 36 (1991), 399–410. MR 1109222
Reference: [15] I. G.  Rosenberg and D.  Schweigert: Compatible orderings and tolerances of lattices.Ann. Discrete Math. 23 (1984), 119–150. MR 0779849
Reference: [16] E. T.  Schmidt: On locally order-polynomially complete modular lattices.Acta Math. Hungar. 49 (1987), 481–486. Zbl 0646.06008, MR 0891060, 10.1007/BF01951011
Reference: [17] D.  Schweigert: Compatible relations of modular and orthomodular lattices.Proc. Amer. Math. Soc. 81 (1981), 462–464. Zbl 0458.06005, MR 0597663, 10.1090/S0002-9939-1981-0597663-5
Reference: [18] D.  Schweigert: Über endliche ordnungspolynomvollständige Verbände.Monatsh. Math. 78 (1974), 68–76. Zbl 0287.06004, MR 0340124, 10.1007/BF01298196
Reference: [19] M.  Stern: Semimodular Lattices, Theory and Applications.Cambridge University Press, Cambridge-New York-Melbourne, 1999. Zbl 0957.06008, MR 1695504
Reference: [20] G.  Szász: Einführung in die Verbändstheorie.Akadémiai Kiadó, Budapest, 1962. MR 0138567
Reference: [21] T.  Tanaka: Canonical subdirect factorization of lattices.J.  Sci. Hiroshima Univ., Ser.  A 16 (1952), 239–246. MR 0060476, 10.32917/hmj/1557367260
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