**
ACTA MATHEMATICA UNIVERSITATIS COMENIANAE **

Vol. 64, 2 (1995)

pp. 273-282

DISTRIBUTIVE LATTICES WHOSE CONGRUENCE LATTICE IS STONE

Z. HELEYOVA

**Abstract**.
Using Priestley's topological duality we characterize bounded distributive lattices with ($L_n$)- and relative ($L_n$)-congruence lattices. In particular, characterizations of bounded distributive lattices with Stone and relative Stone congruence lattices are obtained. Using these descriptions we derive some results of Ref. 8, Ref. 9 Ref. 5 and Ref. 6. In the last section we discuss questions concerning the relation between completeness of a bounded distributive lattice and its minimal Boolean completition. This is connected with a problem of D. Thomas Ref. 9.

**AMS subject classification**.
06D15; Secondary 06D05, 06E1

**Keywords**.
(relative) ($L_n$)-lattice, dual space of a distributive lattice, extremally disconnected space

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