mathematics called order theory, a modular lattice is a lattice that satisfies the following self-dual condition, Modular law a ≤ b implies a ∨ (x ∧ b) =...

examples of modular lattices are the lattice of submodules of a module (hence modular), the lattice of two-sided ideals of a ring, and the lattice of normal...

the modular law is called an orthomodular lattice. In bounded distributive lattices, complements are unique. Every complemented distributive lattice has...

spaces G-module over a group G, in mathematics Modular lattice a kind of partially ordered set Modularity theorem (formerly Taniyama–Shimura conjecture)...

lattice of all subgroups of a group is not a modular lattice in general. Indeed, this particular lattice contains the forbidden "pentagon" N5 as a sublattice...

call this lattice Ln. When n = 8, this is the lattice generated by the roots in the root system called E8. Because there is only one modular form of weight...

utilize to reshape their structures: chain reconfiguration and lattice reconfiguration. Modular robots are usually composed of multiple building blocks of...

coordinate-wise addition or subtraction of two points in the lattice produces another lattice point, that the lattice points are all separated by some minimum distance...

that defines a lattice in the complex plane. This type of lattice is the underlying object with which elliptic functions and modular forms are defined...

T), which is the equation that defines a modular lattice if it holds for any three elements of the lattice with Q ≤ S. In particular, since normal subgroups...

{\mbox{ and }}\quad s=cp+dq.} Elements of the modular group provide a symmetry on the two-dimensional lattice. Let ω1 and ω2 be two complex numbers whose...

fact that a finite lattice is a modular lattice if and only if its Hasse diagram is a modular graph. It is not possible for a modular graph to contain a...

mathematics, a supersolvable lattice is a graded lattice that has a maximal chain of elements, each of which obeys a certain modularity relationship. The definition...

complemented lattices, Heyting algebras etc. Furthermore, every congruence-permutable algebra is congruence-modular, i.e. its lattice of congruences is modular lattice...

technical result on the lattice of subgroups of a group or the lattice of submodules of a module, or more generally for any modular lattice. Lemma. Suppose G...

In mathematics, the Leech lattice is an even unimodular lattice Λ24 in 24-dimensional Euclidean space, which is one of the best models for the kissing...

graph is the graph of this lattice, and has a vertex for each digit sequence. As the graph of a modular lattice, it is a modular graph. The Young–Fibonacci...

positive definite lattice is a modular form whose weight is one half the rank. If the lattice is even, the form has level 1, and if the lattice is odd the form...

relations instead of normal subgroups holds for any algebraic structure. Modular lattice Derek John Scott Robinson (2003). An Introduction to Abstract Algebra...

A metric lattice is modular. 22. A modular lattice is semi-modular. 23. A projective lattice is modular. 24. A projective lattice is geometric. (def)...

g(x)) form the minimal non-modular lattice N5 (see Pic. 1); its appearance prevents the subsumption lattice from being modular and hence also from being...

congruence lattice problem asks whether every algebraic distributive lattice is isomorphic to the congruence lattice of some other lattice. The problem...

semimodular lattice. A finite lattice is modular if and only if it is both upper and lower semimodular. A finite lattice, or more generally a lattice satisfying...

sometimes called the invariant-subspace lattice of T and written Lat(T). As the name suggests, it is a (modular) lattice, with meets and joins given by (respectively)...

mathematics, the E8 lattice is a special lattice in R8. It can be characterized as the unique positive-definite, even, unimodular lattice of rank 8. The name...

random packing of equal spheres generally has a density around 63.5%. A lattice arrangement (commonly called a regular arrangement) is one in which the...

the least element. Modular lattice: a lattice whose elements satisfy the additional modular identity. Distributive lattice: a lattice in which each of meet...

lattice theory, much of which continued using von Neumann's techniques. Birkhoff described this theorem as follows: Any complemented modular lattice L...

axioms. A continuous geometry is a lattice L with the following properties L is modular. L is complete. The lattice operations ∧, ∨ satisfy a certain continuity...

Dense order Distributivity (order theory) Modular lattice Distributive lattice Completely distributive lattice Ascending chain condition Infinite descending...