On atomistic lattices.
Walendziak, Andrzej (1994)
Portugaliae Mathematica
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Walendziak, Andrzej (1994)
Portugaliae Mathematica
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Henry H. Crapo (1967)
Rendiconti del Seminario Matematico della Università di Padova
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Wójtowicz, Marek (2003)
International Journal of Mathematics and Mathematical Sciences
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Zhi-qiang Liu (2024)
Kybernetika
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In this article, we investigate the algebraic structures of the partial orders induced by uninorms on a bounded lattice. For a class of uninorms with the underlying drastic product or drastic sum, we first present some conditions making a bounded lattice also a lattice with respect to the order induced by such uninorms. And then we completely characterize the distributivity of the lattices obtained.
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].