On atomistic lattices.
Walendziak, Andrzej (1994)
Portugaliae Mathematica
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Walendziak, Andrzej (1994)
Portugaliae Mathematica
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Josef Niederle (1989)
Czechoslovak Mathematical Journal
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Václav Slavík (1973)
Commentationes Mathematicae Universitatis Carolinae
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Henry H. Crapo (1967)
Rendiconti del Seminario Matematico della Università di Padova
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Yuichi Futa, Yasunari Shidama (2016)
Formalized Mathematics
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In this article, we formalize the definition of lattice of ℤ-module and its properties in the Mizar system [5].We formally prove that scalar products in lattices are bilinear forms over the field of real numbers ℝ. We also formalize the definitions of positive definite and integral lattices and their properties. Lattice of ℤ-module is necessary for lattice problems, LLL (Lenstra, Lenstra and Lovász) base reduction algorithm [14], and cryptographic systems with lattices [15] and coding...
Ladislav Beran (1975)
Acta Universitatis Carolinae. Mathematica et Physica
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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].
Ivan Chajda, Helmut Länger (2017)
Topological Algebra and its Applications
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We show that every idempotent weakly divisible residuated lattice satisfying the double negation law can be transformed into an orthomodular lattice. The converse holds if adjointness is replaced by conditional adjointness. Moreover, we show that every positive right residuated lattice satisfying the double negation law and two further simple identities can be converted into an orthomodular lattice. In this case, also the converse statement is true and the corresponence is nearly one-to-one. ...