``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

DOI:
https://doi.org/10.1090/S0002-9939-1993-1150651-0

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:
https://doi.org/10.1090/S0002-9939-1993-1150651-0

Keywords:
Complete lattice,
distributive lattice,
complete congruence,
congruence lattice

Article copyright:
© Copyright 1993
American Mathematical Society