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Distributive lattices with an operator. (English) Zbl 0854.06016

A \(j\)-distributive lattice is an algebra \((L, \vee, \wedge,j, 0, 1)\) such that \((L, \vee, \wedge, 0, 1)\) is a bounded distributive lattice and \(j : L \to L\) is a join-homomorphism. Congruences of \(j\)-distributive lattices are described in terms of corresponding dual spaces, and simple and subdirectly irreducible algebras are characterized for several conditions imposed on \(j\).
Reviewer: J.Niederle (Brno)

MSC:

06D99 Distributive lattices
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References:

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