Mathematical logic | Ordered algebraic structures | Lattice theory | Fuzzy logic

Residuated lattice

In abstract algebra, a residuated lattice is an algebraic structure that is simultaneously a lattice x ≤ y and a monoid x•y which admits operations x\z and z/y, loosely analogous to division or implication, when x•y is viewed as multiplication or conjunction, respectively. Called respectively right and left residuals, these operations coincide when the monoid is commutative. The general concept was introduced by Morgan Ward and Robert P. Dilworth in 1939. Examples, some of which existed prior to the general concept, include Boolean algebras, Heyting algebras, residuated Boolean algebras, relation algebras, and MV-algebras. Residuated semilattices omit the meet operation ∧, for example Kleene algebras and action algebras. (Wikipedia).

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Lattice Structures in Ionic Solids

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From playlist General Chemistry

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Recursively Defined Sets - An Intro

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From playlist All Things Recursive - with Math and CS Perspective

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From playlist Atomic Structures and Bonding

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Close Packing Crystal Structures

A description of the two types of crystal structures created from close-packed planes.

From playlist Atomic Structures and Bonding

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Linear Desface

Here we show a quick way to set up a face in desmos using domain and range restrictions along with sliders. @shaunteaches

From playlist desmos

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We introduce lattices and integral linear spans of vexels. These are remarkably flexible, common and useful algebraic objects, and they are the direct integral analogs of vector spaces. To understand the structure of a given lattice, the algorithm to compute a Hermite normal form basis is

From playlist Math Foundations

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This video shows you how a matrix is constructed from a set of linear equations. It helps you understand where the various elements in a matrix comes from.

From playlist Linear Algebra

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Mod-01 Lec-05 Introduction to Nanomaterials

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From playlist IIT Kanpur: Nanostructures and Nanomaterials | CosmoLearning.org

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Crystal lattice and unit cell

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From playlist Materials Sciences 101 - Introduction to Materials Science & Engineering 2020

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From playlist Number Theory

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From playlist Complex analysis

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From playlist Conference and School on Nucleation Aggregation and Growth

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From playlist Number Theory

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From playlist Mathematics

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From playlist IIT Kanpur: Nanostructures and Nanomaterials | CosmoLearning.org

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Specialization of difference equations ... - H. Hrushovski - Workshop 2 - CEB T1 2018

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From playlist 2018 - T1 - Model Theory, Combinatorics and Valued fields

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From playlist HIM Lectures: Junior Trimester Program "Algebraic Geometry"

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From playlist SpoonFeedMe: Concrete Structures

Related pages

Action algebra | Algebraic structure | Relevance logic | Annihilator (ring theory) | Ideal (ring theory) | Monus | Morgan Ward | Substructural logic | Peirce's law | Robert P. Dilworth | Lattice (order) | Tautology (logic) | Commutative algebra | Total order | Residuated Boolean algebra | Formal language | Distributive lattice | Residuated mapping | Mathematics | Linear logic | Conductor (ring theory) | Relation algebra | Residuated lattice | Ring (mathematics) | MV-algebra | Galois connection | Variety (universal algebra) | Abstract algebra | Quantale | Kleene algebra | Heyting algebra | Monoid | Boolean algebra (structure)