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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

``Complete-simple'' distributive lattices


Authors: G. Grätzer and E. T. Schmidt
Journal: Proc. Amer. Math. Soc. 119 (1993), 63-69
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 two-element chain. We can generalize the concept of a simple lattice to complete lattices as follows: a complete lattice is complete-simple if it has only the two trivial complete congruences. In this paper we show the existence of infinite complete-simple distributive lattices.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1150651-0
PII: S 0002-9939(1993)1150651-0
Keywords: Complete lattice, distributive lattice, complete congruence, congruence lattice
Article copyright: © Copyright 1993 American Mathematical Society