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The concept of a lattice arises in order theory, a branch of mathematics. The Hasse diagram below depicts the inclusion relationships among some important subclasses of lattices.
Diagram showing implications of common lattice properties
relationships among some important subclasses oflattices. 1. A boolean algebra is a complemented distributive lattice. (def) 2. A boolean algebra is a heyting...
A coupled maplattice (CML) is a dynamical system that models the behavior of nonlinear[disambiguation needed] systems (especially partial differential...
called an orthomodular lattice. In bounded distributive lattices, complements are unique. Every complemented distributive lattice has a unique orthocomplementation...
A mind map is a diagram used to visually organize information into a hierarchy, showing relationships among pieces of the whole. It is often created around...
counterclockwise Lattices, partial orders in which each pair of elements has a greatest lower bound and a least upper bound. Many different types oflattice have...
functors from the category of frames and frame-homomorphisms, and from the category of distributive lattices and lattice-homomorphisms, have a left adjoint...
Modeling Language formalism. Topic maps: Both concept maps and topic maps are kinds of knowledge graph, but topic maps were developed by information management...
law and whose morphisms were maps which preserved finite meets and arbitrary joins. He called such lattices "local lattices"; today they are called "frames"...
distributive law; in the case oflattices, they are linked by the absorption law. Ringoids also tend to have numerical models, while lattices tend to have set-theoretic...
element of a PID has a unique decomposition into prime elements (so an analogue of the fundamental theorem of arithmetic holds); any two elements of a PID...
irreducible elements of R and w is a unit such that x = w q1 q2 ⋅⋅⋅ qm with m ≥ 0, then m = n, and there exists a bijective map φ : {1, ..., n} → {1,...
identity elements are the lattice's top and its bottom, respectively. Being lattices, Heyting algebras and Boolean algebras are endowed with these monoid structures...
takes an algebraic element α to the product of all the conjugates of α. This norm maps the ring of integers of a number field K, say OK, to the nonnegative...
A topic map is a standard for the representation and interchange of knowledge, with an emphasis on the findability of information. Topic maps were originally...
free; that is, it has a basis, and all bases of a module have the same number of elements. Linear maps between finite-dimensional modules over a division...
generalizations of modularity related to this notion and to semimodularity. Modular lattices are sometimes called Dedekind lattices after Richard Dedekind...
terms of Galois theory, this means that GF(pn) is a Galois extension of GF(p), which has a cyclic Galois group. The fact that the Frobenius map is surjective...
lattice without the assumption of finiteness. Geometric lattices and matroid lattices, respectively, form the latticesof flats of finite, or finite and infinite...
homomorphism of K-algebras or K-algebra homomorphism is a K-linear map f: A → B such that f(xy) = f(x) f(y) for all x, y in A. The space of all K-algebra...
combination of them. If dim V = dim W, a 1-to-1 correspondence between fixed bases of V and W gives rise to a linear map that maps any basis element of V to...
A cognitive map is a type of mental representation which serves an individual to acquire, code, store, recall, and decode information about the relative...
factors into a product of prime ideals. It can be shown that such a factorization is then necessarily unique up to the order of the factors. There are...
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