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Algebras whose principal congruences form a sublattice of the congruence lattice. (English) Zbl 0668.08003
It is known that principal congruences do not form a sublattice of the congruence lattice in general. The author proves the following two theorems: Theorem 1. Let D be a distributive lattice with least element 0. The set of all principal congruences \(\Theta\) (x,0), \(x\in D\), forms a sublattice of Con D. Theorem 2. Let d be a weakly regular distributive lattice with least element 0. The set of all principal congruences of D forms a sublattice of Con D.
Reviewer: J.Duda

MSC:
08A30 Subalgebras, congruence relations
06D05 Structure and representation theory of distributive lattices
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References:
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