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Jacobi identities, modular lattices, and modular towers
European Journal of Combinatorics, 2004 There are proved generalized Jacobi identities related to odd diagonal lattices. Particular cases of lattices give some known Jacobi identities. In [Trans. Am. Math. Soc. 355, 1005--1520 (2003; Zbl 1021.11036)] the Jacobi identities were used to derive quadratic iteration that generalize the AGM iteration in the classical case.
Chua, K.S., Solé, P.
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Journal of Combinatorial Theory, Series A, 1982 AbstractLet L be a finite lattice. A map f of the join irreducible elements of L to the meet irreducible elements of L is called a matching of L if f is one-to-one and x⩽f(x) for each join irreducible x. We investigate this conjecture: every finite modular lattice has a matching. The conjecture is verified for certain classes of modular lattices.
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SciPost PhysicsLevin--Wen models are a class of two-dimensional lattice spin models with a Hamiltonian that is a sum of commuting projectors, which describe topological phases of matter related to Drinfeld centres.
Vincentas Mulevičius, Ingo Runkel, Thomas Voß
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Locally modular lattices and locally distributive lattices [PDF]
Proceedings of the American Mathematical Society, 1974 A locally modular (resp. locally distributive) lattice is a lattice with a congruence relation and each of whose equivalence class has sufficiently many elements and is a modular (resp. distributive) sublattice. Both the lattice of all closed subspaces of a locally convex space and the lattice of projections of a locally finite von
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Modularity, Atomicity and States in Archimedean Lattice Effect Algebras
Symmetry, Integrability and Geometry: Methods and Applications, 2010 Effect algebras are a generalization of many structures which arise in quantum physics and in mathematical economics. We show that, in every modular Archimedean atomic lattice effect algebra E that is not an orthomodular lattice there exists an (o ...
Jan Paseka
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Design and fabrication of modular tensegrity-like lattices with auxetic properties
Materials & DesignTensegrity-like lattices have recently been found to feature a nonlinear mechanical response descending from that of the corresponding tensegrity structures.
Anna Al Sabouni-Zawadzka +3 more
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Geometric Lattice Structure of Covering-Based Rough Sets through Matroids
Journal of Applied Mathematics, 2012 Covering-based rough set theory is a useful tool to deal with inexact, uncertain, or vague knowledge in information systems. Geometric lattice has been widely used in diverse fields, especially search algorithm design, which plays an important role in ...
Aiping Huang, William Zhu
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Ojective ideals in modular lattices [PDF]
Czechoslovak Mathematical Journal, 2015 In this paper the concept of an extending ideal in a modular lattice is introduced. A translation of module-theoretical concept of ojectivity (i.e. generalized relative injectivity) in the context of the lattice of ideals of a modular lattice is introduced.
Nimbhorkar, Shriram K., Shroff, Rupal C.
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Archimedean Atomic Lattice Effect Algebras with Complete Lattice of Sharp Elements
Symmetry, Integrability and Geometry: Methods and Applications, 2010 We study Archimedean atomic lattice effect algebras whose set of sharp elements is a complete lattice. We show properties of centers, compatibility centers and central atoms of such lattice effect algebras.
Zdenka Riecanová
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Journal of New Results in Science, 2012 Soft set theory was introduced by Molodtsov in 1999 as a general mathematical tool for dealing with problems that contain uncertainity. In this paper,we define concept of a soft lattice, soft sublattice, complete soft lattice, modular soft lattice ...
Faruk Karaaslan +2 more
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