Residuated closure operators
Janowitz, M.F. (1967)
Portugaliae mathematica
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Displaying similar documents to “Note on complemented closure operators of complete lattices”
Residuated closure operators
On atomistic lattices.
Walendziak, Andrzej (1994)
Portugaliae Mathematica
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On completely meet-irreducible elements in compactly generated lattices
Josef Niederle (1989)
Czechoslovak Mathematical Journal
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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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On skew lattices. II.
Václav Slavík (1973)
Commentationes Mathematicae Universitatis Carolinae
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The lattice of pseudotopologies on S
Carstens, Allan M. (1973)
Portugaliae mathematica
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Dual Lattice of ℤ-module Lattice
Yuichi Futa, Yasunari Shidama (2017)
Formalized Mathematics
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In this article, we formalize in Mizar [5] the definition of dual lattice and their properties. We formally prove that a set of all dual vectors in a rational lattice has the construction of a lattice. We show that a dual basis can be calculated by elements of an inverse of the Gram Matrix. We also formalize a summation of inner products and their properties. Lattice of ℤ-module is necessary for lattice problems, LLL(Lenstra, Lenstra and Lovász) base reduction algorithm and cryptographic...