lattice module
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Lattice (order) — See also: Lattice (group) The name lattice is suggested by the form of the Hasse diagram depicting it. Shown here is the lattice of partitions of a four element set {1,2,3,4}, ordered by the relation is a refinement of . In mathematics, a… … Wikipedia
Module (mathematics) — For other uses, see Module (disambiguation). In abstract algebra, the concept of a module over a ring is a generalization of the notion of vector space, wherein the corresponding scalars are allowed to lie in an arbitrary ring. Modules also… … Wikipedia
Congruence lattice problem — In mathematics, the congruence lattice problem asks whether every algebraic distributive lattice is isomorphic to the congruence lattice of some other lattice. The problem was posed by Robert P. Dilworth, and for many years it was one of the most … Wikipedia
Modular lattice — Hasse diagram of N5, the smallest non modular lattice. In the branch of mathematics called order theory, a modular lattice is a lattice that satisfies the following self dual condition: Modular law x ≤ b implies… … Wikipedia
Demazure module — In mathematics, a Demazure module, introduced by Demazure (1974a, 1974b). is a submodule of a finite dimensional representation generated by an extremal weight space under the action of a Borel subalgebra. The Demazure character formula,… … Wikipedia
Complete lattice — In mathematics, a complete lattice is a partially ordered set in which all subsets have both a supremum (join) and an infimum (meet). Complete lattices appear in many applications in mathematics and computer science. Being a special instance of… … Wikipedia
Unimodular lattice — In mathematics, a unimodular lattice is a lattice of discriminant 1 or −1.The E 8 lattice and the Leech lattice are two famous examples. Definitions *A lattice is a free abelian group of finite rank with an integral symmetric bilinear form (·,·) … Wikipedia
Finitely generated module — In mathematics, a finitely generated module is a module that has a finite generating set. Equivalently, it is a homomorphic image of a free module on finitely many generators. The kernel of this homomorphism need not be finitely generated (then… … Wikipedia
Self-reconfiguring modular robot — Modular self reconfiguring robotic systems or self reconfigurable modular robots are autonomous kinematic machines with variable morphology. Beyond conventional actuation, sensing and control typically found in fixed morphology robots, self… … Wikipedia
Outline of algebraic structures — In universal algebra, a branch of pure mathematics, an algebraic structure is a variety or quasivariety. Abstract algebra is primarily the study of algebraic structures and their properties. Some axiomatic formal systems that are neither… … Wikipedia
List of algebraic structures — In universal algebra, a branch of pure mathematics, an algebraic structure is a variety or quasivariety. Abstract algebra is primarily the study of algebraic structures and their properties. Some axiomatic formal systems that are neither… … Wikipedia
