On atomistic lattices.
Walendziak, Andrzej (1994)
Portugaliae Mathematica
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Displaying similar documents to “Freely adjoining a complement to a lattice”
On atomistic lattices.
Indexed annihilators in lattices
Ivan Chajda (1995)
Archivum Mathematicum
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The concept of annihilator in lattice was introduced by M. Mandelker. Although annihilators have some properties common with ideals, the set of all annihilators in need not be a lattice. We give the concept of indexed annihilator which generalizes it and we show the basic properties of the lattice of indexed annihilators. Moreover, distributive and modular lattices can be characterized by using of indexed annihilators.
Reflections and coreflections in generalized orthomodular lattices
Ladislav Beran (1975)
Acta Universitatis Carolinae. Mathematica et Physica
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Structure theory for geometric lattices
Henry H. Crapo (1967)
Rendiconti del Seminario Matematico della Università di Padova
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Congruences on finite lattices
Bohuslav Sivák (1982)
Mathematica Slovaca
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Finite atomistic lattices that can be represented as lattices of quasivarieties
K. Adaricheva, Wiesław Dziobiak, V. Gorbunov (1993)
Fundamenta Mathematicae
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We prove that a finite atomistic lattice can be represented as a lattice of quasivarieties if and only if it is isomorphic to the lattice of all subsemilattices of a finite semilattice. This settles a conjecture that appeared in the context of [11].