How many four-generated simple lattices
Ivan Rival, Bill Sands (1982)
Banach Center Publications
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Ivan Rival, Bill Sands (1982)
Banach Center Publications
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Václav Slavík (1980)
Commentationes Mathematicae Universitatis Carolinae
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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].
Büchi, J. Richard (1952)
Portugaliae mathematica
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Ladislav Beran (1975)
Acta Universitatis Carolinae. Mathematica et Physica
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Stern, Manfred (1989)
Portugaliae mathematica
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Henry H. Crapo (1967)
Rendiconti del Seminario Matematico della Università di Padova
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Radomír Halaš (2002)
Discussiones Mathematicae - General Algebra and Applications
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It is well known that every complete lattice can be considered as a complete lattice of closed sets with respect to appropriate closure operator. The theory of q-lattices as a natural generalization of lattices gives rise to a question whether a similar statement is true in the case of q-lattices. In the paper the so-called M-operators are introduced and it is shown that complete q-lattices are q-lattices of closed sets with respect to M-operators.