Congruence Lattices of Semilattices with Operators
| Autor: | Joy Nishida, James B. Nation, Jennifer Hyndman |
|---|---|
| Rok vydání: | 2015 |
| Předmět: |
Mathematics::General Mathematics
Logic High Energy Physics::Lattice Mathematics::Rings and Algebras 010102 general mathematics Semilattice 0102 computer and information sciences 01 natural sciences Congruence lattice problem Combinatorics Mathematics::Logic Operator (computer programming) History and Philosophy of Science 010201 computation theory & mathematics Lattice (order) 0101 mathematics Algebraic number Mathematics |
| Zdroj: | Studia Logica. 104:305-316 |
| ISSN: | 1572-8730 0039-3215 |
| Popis: | 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 $${{\rm Con}(S,+,0,G) \cong^{d} {{\rm S}_{p}}(L,H)}$$Con(S,+,0,G)?dSp(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 Jonsson---Kiefer property. |
| Databáze: | OpenAIRE |
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