``Completesimple'' distributive lattices
Authors:
G. Grätzer and E. T. Schmidt
Journal:
Proc. Amer. Math. Soc. 119 (1993), 6369
MSC:
Primary 06B15; Secondary 06B10, 06D05
MathSciNet review:
1150651
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Abstract: It is well known that the only simple distributive lattice is the twoelement chain. We can generalize the concept of a simple lattice to complete lattices as follows: a complete lattice is completesimple if it has only the two trivial complete congruences. In this paper we show the existence of infinite completesimple distributive lattices.
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 , The complete congruence lattice of a complete lattice, Lattices, Semigroups, and Universal Algebra, Proceedings of an International Conference on Lattices, Semigroups, and Universal Algebra (Lisbon, 1988), Plenum Press, New York and London, 1990, pp. 8188. MR 1085069
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 , A lattice theoretic proof of the independence of the automorphism group, the congruence lattice, and subalgebra lattice of an infinitary algebra, Algebra Universalis 27 (1990), 466473. MR 1387894 (97a:08011)
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 G. Grätzer and H. Lakser, On complete congruence lattices of complete lattices, Trans. Amer. Math. Soc. 327 (1991), 385405. MR 1036003 (92e:06019)
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 , On congruence lattices of complete lattices, J. Austral. Math. Soc. Ser. A 52 (1992), 5787. MR 1137597 (92m:06014)
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 K. Reuter and R. Wille, Complete congruence relations of complete lattices, Acta Sci. Math. (Szeged) 51 (1987), 319327. MR 940936 (89d:06009)
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 S.K. Teo, Representing finite lattices as complete congruence lattices of complete lattices, Ann. Univ. Sci. Budapest. Eötvös Sect. Math. 33 (1990), 177182. MR 1139362 (92j:06010)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939199311506510
PII:
S 00029939(1993)11506510
Keywords:
Complete lattice,
distributive lattice,
complete congruence,
congruence lattice
Article copyright:
© Copyright 1993 American Mathematical Society
