Designing modular and distributive lattices using L-soft group: A survey
نویسندگان
چکیده
منابع مشابه
locally modular lattices and locally distributive lattices
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 Neumann algebra are locally modular. The lattice of all /^-topo...
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In 1990, we published the following result: Let m be a regular cardinal > א0. Every m-algebraic lattice L can be represented as the lattice of m-complete congruence relations of an m-complete modular lattice K. In this note, we present a short proof of this theorem. In fact, we present a significant improvement: The lattice K we construct is 2-distributive.
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A resolution of the intersection of a finite number of subgroups of an abelian group by means of their sums is constructed, provided the lattice generated by these subgroups is distributive. This is used for detecting singularities of modules over Dedekind rings. A generalized Chinese remainder theorem is derived as a consequence of the above resolution. The GelfandNaimark duality between finit...
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A modular semilattice is a semilattice S in which w > a A ft implies that there exist i,jeS such that x > a. y > b and x A y = x A w. This is equivalent to modularity in a lattice and in the semilattice of ideals of the semilattice, and the condition implies the Kurosh-Ore replacement property for irreducible elements in a semilattice. The main results provide extensions of the classical charac...
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To any entailment relation Sco74] we associate a distributive lattice. We use this to give a construction of the product of lattices over an arbitrary index set, of the Vietoris construction, of the embedding of a distributive lattice in a boolean algebra, and to give a logical description of some spaces associated to mathematical structures.
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ژورنال
عنوان ژورنال: International Journal of Engineering & Technology
سال: 2017
ISSN: 2227-524X
DOI: 10.14419/ijet.v7i1.3.9227