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

finite lattice representation problem, or finite congruence lattice problem, asks whether every finite lattice is isomorphic to the congruence lattice of...

generating Maltsev conditions associated with congruence identities. Quotient ring Congruence lattice problem Lattice of subgroups A. G. Kurosh, Lectures on...

groups is the congruence subgroup problem, which asks whether all subgroups of finite index are essentially congruence subgroups. Congruence subgroups of...

rings, vector spaces, modules, semigroups, lattices, and so forth. The common theme is that a congruence is an equivalence relation on an algebraic object...

COIN-OR Linear Program Solver Communication Linking Protocol Congruence lattice problem Constraint Logic Programming Constraint logic programming (Real)...

Farrell–Jones conjecture Finite lattice representation problem: is every finite lattice isomorphic to the congruence lattice of some finite algebra? Goncharov...

that θ is distributive, if it is a join, in the congruence lattice Con S of S, of monomial join-congruences of S. The following definition originates in...

vertically symmetrical number. 25 is the smallest pseudoprime satisfying the congruence 7n = 7 mod n. 25 is the smallest aspiring number — a composite non-sociable...

arithmetic lattices in higher-rank groups have the congruence subgroup property but there are many lattices in S O ( n , 1 ) , S U ( n , 1 ) {\displaystyle...

structure. In general, congruence relations play the role of kernels of homomorphisms, and the quotient of a structure by a congruence relation can be formed...

semigroup congruence ~ induces congruence classes [a]~ = {x ∈ S | x ~ a} and the semigroup operation induces a binary operation ∘ on the congruence classes:...

has been applied recently in solving several lattice theory problems, such as the congruence lattice problem. Denote by [ X ] < ω {\displaystyle [X]^{<\omega...

Hungarian-American mathematician whose research concerns clones, the congruence lattice problem, and other topics in universal algebra. She is a professor of...

The Basel problem is a problem in mathematical analysis with relevance to number theory, concerning an infinite sum of inverse squares. It was first posed...

structural information and can be used for determining, e.g., the congruence relations of the lattice. Triadic concept analysis replaces the binary incidence relation...

This is denoted as z1 ≡ z2 (mod z0). The congruence modulo z0 is an equivalence relation (also called a congruence relation), which defines a partition of...

Unimodular lattice Fermat's theorem on sums of two squares Proofs of Fermat's theorem on sums of two squares Riemann zeta function Basel problem on ζ(2)...

center Hyperplane Lattice Ehrhart polynomial Leech lattice Minkowski's theorem Packing Sphere packing Kepler conjecture Kissing number problem Honeycomb Andreini...

positive integer. These are always finite-index subgroups and the congruence subgroup problem roughly asks whether all subgroups are obtained in this way....

operator Binary operation Commutative Congruence relation Equivalence class Equivalence relation Lattice (group) Lattice (discrete subgroup) Multiplication...

defines an integer triangle that is unique up to congruence. So the number of integer triangles (up to congruence) with perimeter p is the number of partitions...

smallest congruence on S such that S/σ is a group, that is, if τ is any other congruence on S with S/τ a group, then σ is contained in τ. The congruence σ is...

Digital Calculating Machinery: 141–146. Thomson, W. E. (1958). "A Modified Congruence Method of Generating Pseudo-random Numbers". The Computer Journal. 1 (2):...

foundation for geometry, treated congruence as an undefined term whose properties are defined by axioms. Congruence and similarity are generalized in...

suggested by Birkhoff's papers, dealing with free algebras, congruence and subalgebra lattices, and homomorphism theorems. Although the development of mathematical...

and the opposite angles of a parallelogram are of equal measure. The congruence of opposite sides and opposite angles is a direct consequence of the Euclidean...

(n)}=m(m^{\varphi (n)})^{h}\equiv m(1)^{h}\equiv m{\pmod {n}},} where the second-last congruence follows from Euler's theorem. More generally, for any e and d satisfying...

Lattice (group) Lattice (discrete subgroup) Frieze group Wallpaper group Space group Crystallographic group Fuchsian group Modular group Congruence subgroup...

computer programs, based on monotonic functions over ordered sets, especially lattices. It can be viewed as a partial execution of a computer program which gains...