``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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 , 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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 , 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
