Voronoĭ type criteria for lattice coverings with balls
Peter M. Gruber (2011)
Acta Arithmetica
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Peter M. Gruber (2011)
Acta Arithmetica
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Sándor Radeleczki (2002)
Discussiones Mathematicae - General Algebra and Applications
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We define and study classification systems in an arbitrary CJ-generated complete lattice L. Introducing a partial order among the classification systems of L, we obtain a complete lattice denoted by Cls(L). By using the elements of the classification systems, another lattice is also constructed: the box lattice B(L) of L. We show that B(L) is an atomistic complete lattice, moreover Cls(L)=Cls(B(L)). If B(L) is a pseudocomplemented lattice, then every classification system of L is independent...
Kołodziejczyk, Krzysztof (1999)
Beiträge zur Algebra und Geometrie
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Jaroslav Ježek (1981)
Czechoslovak Mathematical Journal
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Cohn, Henry, Kumar, Abhinav (2004)
Electronic Research Announcements of the American Mathematical Society [electronic only]
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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...
M. Nesibe Kesicioğlu (2017)
Kybernetika
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In this paper, an equivalence on the class of nullnorms on a bounded lattice based on the equality of the orders induced by nullnorms is introduced. The set of all incomparable elements w.r.t. the order induced by nullnorms is investigated. Finally, the recently posed open problems have been solved.
J. L. Ericksen (1982)
Rendiconti del Seminario Matematico della Università di Padova
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R. J. Hans-Gill, Madhu Raka, Ranjeet Sehmi (2011)
Acta Arithmetica
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Emel Aşıcı, Funda Karaçal (2016)
Kybernetika
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In this paper, we define the set of incomparable elements with respect to the triangular order for any t-norm on a bounded lattice. By means of the triangular order, an equivalence relation on the class of t-norms on a bounded lattice is defined and this equivalence is deeply investigated. Finally, we discuss some properties of this equivalence.
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. ...