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SLOGICA
2016

Congruence Lattices of Semilattices with Operators

3 years 10 days ago
Congruence Lattices of Semilattices with Operators
Abstract. The duality between congruence lattices of semilattices, and algebraic subsets of an algebraic lattice, is extended to include semilattices with operators. For a set G of operators on a semilattice S, we have Con(S, +, 0, G) ∼=d Sp(L, H), where L is the ideal lattice of S, and H is a corresponding set of adjoint maps on L. This duality is used to find some representations of lattices as congruence lattices of semilattices with operators. It is also shown that these congruence lattices satisfy the J´onsson-Kiefer property.
Jennifer Hyndman, James B. Nation, Joy Nishida
Added 09 Apr 2016
Updated 09 Apr 2016
Type Journal
Year 2016
Where SLOGICA
Authors Jennifer Hyndman, James B. Nation, Joy Nishida
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