“Complete-simple” distributive lattices

Grätzer, G.; Schmidt, E. T.

doi:10.1090/S0002-9939-1993-1150651-0

“Complete-simple” distributive lattices
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by G. Grätzer and E. T. Schmidt PDF

Proc. Amer. Math. Soc. 119 (1993), 63-69 Request permission

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.

References

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