Cocompact lattices.
Călugăreanu, Grigore (1996)
Mathematica Pannonica
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Călugăreanu, Grigore (1996)
Mathematica Pannonica
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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].
Walendziak, Andrzej (1994)
Portugaliae Mathematica
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Ladislav Beran (1975)
Acta Universitatis Carolinae. Mathematica et Physica
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Henry H. Crapo (1967)
Rendiconti del Seminario Matematico della Università di Padova
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Ivan Rival, Bill Sands (1982)
Banach Center Publications
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Ramalho, Margarita (1990)
Portugaliae mathematica
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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...