A closer look at some new identities.
Campbell, Geoffrey B. (1998)
International Journal of Mathematics and Mathematical Sciences
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Campbell, Geoffrey B. (1998)
International Journal of Mathematics and Mathematical Sciences
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Campbell, Geoffrey B. (1994)
International Journal of Mathematics and Mathematical Sciences
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J. L. Ericksen (1982)
Rendiconti del Seminario Matematico della Università di Padova
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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...
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. ...
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...
Walendziak, Andrzej (1994)
Portugaliae Mathematica
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Christian Krattenthaler (1989)
Manuscripta mathematica
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Alfonz Haviar (1979)
Mathematica Slovaca
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