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Distributive lattices with an operator
Studia Logica, 1996A \(j\)-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
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Distributive PBZ$$^{*}$$-lattices
Studia LogicazbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Subordinations on Bounded Distributive Lattices
Order, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Distributive Lattices Lattice-Groups
2015This chapter begins with an introductory section which fixes the formal algebraic framework of distributive lattices and of Boolean algebras.
Henri Lombardi, Claude Quitté
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On Unification for Bounded Distributive Lattices
ACM Transactions on Computational Logic, 2000We give a method for deciding unifiability in the variety of bounded distributive lattices. For this, we reduce the problem of deciding whether a unification problem S has a solution to the problem of checking the satisfiability of a set Φ S of ground clauses.
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ENDOMORPHISMS OF DISTRIBUTIVE LATTICES WITH A QUANTIFIER
International Journal of Algebra and Computation, 2007Let V be a non-trivial variety of bounded distributive lattices with a quantifier, as introduced by Cignoli in [7]. It is shown that if V does not contain the 4-element bounded Boolean lattice with a simple quantifier, then V contains non-isomorphic algebras with isomorphic endomorphism monoids, but there are always at most two such algebras. Further,
M. E. Adams, Wieslaw Dziobiak
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Homogeneous Modular Lattices are Distributive
Order, 2015A structure \(A\) is homogeneous if any partial isomorphism between finitely generated substructures can be extended to an automorphism of the structure \(A\). \textit{A. Abogatma} and \textit{J. K. Truss} [Order 32, No. 2, 239--243 (2015; Zbl 1348.06004)] have constructed uncountably many contable homogeneous lattices.
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On Weak Lewis Distributive Lattices
Studia LogicazbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ismael Calomino +2 more
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Studia Logica, 1996
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Distributive Lattices with a Dual Endomorphism
Mathematical Logic Quarterly, 1985An Ockham algebra is a bounded lattice L on which there is defined a \(\{\) 0,1\(\}\)-exchanging dual endomorphism f. The author considers here distributive Ockham algebras in which \(f^ 3=f\). A complete description of the subdirectly irreducible algebras is given.
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