relationships among some important subclasses of lattices. 1. A boolean algebra is a complemented distributive lattice. (def) 2. A boolean algebra is a heyting...

A coupled map lattice (CML) is a dynamical system that models the behavior of nonlinear systems (especially partial differential equations). They are...

called an orthomodular lattice. In bounded distributive lattices, complements are unique. Every complemented distributive lattice has a unique orthocomplementation...

respective operations of the arithmetic lattice. This is the specific property that distinguishes arithmetic lattices from algebraic lattices, for which the...

functors from the category of frames and frame-homomorphisms, and from the category of distributive lattices and lattice-homomorphisms, have a left adjoint...

counterclockwise Lattices, partial orders in which each pair of elements has a greatest lower bound and a least upper bound. Many different types of lattice have...

an infimum. Every non-empty finite lattice is complete, but infinite lattices may be incomplete. Complete lattices appear in many applications in mathematics...

binary operations. In the case of ringoids, the two operations are linked by the distributive law; in the case of lattices, they are linked by the absorption...

A mind map is a diagram used to visually organize information into a hierarchy, showing relationships among pieces of the whole. It is often based on a...

law and whose morphisms were maps which preserved finite meets and arbitrary joins. He called such lattices "local lattices"; today they are called "frames"...

, qm are irreducible elements of R such that x = q1 q2 ⋅⋅⋅ qm with m ≥ 1, then m = n, and there exists a bijective map φ : {1, ..., n} → {1, ..., m} such...

proofs. Given K-algebras A and B, a 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...

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...

map from M to M. Applying the structure theorem for finitely generated modules over a principal ideal domain to this example shows the existence of the...

orthocomplemented lattice. Orthocomplemented lattices arise naturally in quantum logic as lattices of closed linear subspaces for separable Hilbert spaces. List of Boolean...

Modeling Language formalism. Topic maps: Both concept maps and topic maps are kinds of knowledge graph, but topic maps were developed by information management...

element of a PID has a unique factorization into prime elements (so an analogue of the fundamental theorem of arithmetic holds); any two elements of a PID...

Tamari Lattices and Related Structures: Tamari Memorial Festschrift, Springer, p. 11, ISBN 978-3-0348-0405-9. Evseev, A. E. (1988), "A survey of partial...

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...

identity map of the additive structure of ⁠ Z / 2 Z {\displaystyle \mathbb {Z} /2\mathbb {Z} } ⁠. Intuitively, a graded monoid is the subset of a graded...

the same time, semirings are a generalization of bounded distributive lattices. The smallest semiring that is not a ring is the two-element Boolean algebra...

identity elements are the lattice's top and its bottom, respectively. Being lattices, Heyting algebras and Boolean algebras are endowed with these monoid structures...

of any collection of subsemigroups of S is also a subsemigroup of S. So the subsemigroups of S form a complete lattice. An example of a semigroup with...

generalizations of modularity related to this notion and to semimodularity. Modular lattices are sometimes called Dedekind lattices after Richard Dedekind...

variants of the definition of "domain". The ring Z / 6 Z {\displaystyle \mathbb {Z} /6\mathbb {Z} } is not a domain, because the images of 2 and 3 in...

of knots, they can be viewed as algebraic constructions in their own right. In particular, the definition of a quandle axiomatizes the properties of conjugation...

characters, one uses the map α k ↦ exp ⁡ ( 2 π i k / ( q − 1 ) ) {\displaystyle \alpha ^{k}\mapsto \exp(2\pi ik/(q-1))} to map eigenvalues of a representation...

distributive lattices states that the elements of any finite distributive lattice can be represented as finite sets, in such a way that the lattice operations...

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 topic map is a standard for the representation and interchange of knowledge, with an emphasis on the findability of information. Topic maps were originally...