The Dimension Lattice of a JBW-Algebra.
Klaus Alvermann (1987)
Mathematische Zeitschrift
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Klaus Alvermann (1987)
Mathematische Zeitschrift
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Graham J. Wood (1973)
Mathematische Zeitschrift
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Graham J.O. Jameson (1967)
Mathematische Zeitschrift
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Wójtowicz, Marek (2003)
International Journal of Mathematics and Mathematical Sciences
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Rudolf-E. Hoffmann (1982)
Mathematische Zeitschrift
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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...
Rosalind Reichard (1972)
Mathematische Zeitschrift
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Wolfgang Arendt (1984)
Mathematische Zeitschrift
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Jaroslav Ježek (1981)
Czechoslovak Mathematical Journal
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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...
Paul C. Shields (1967)
Mathematische Zeitschrift
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