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Morita equivalence

In abstract algebra, Morita equivalence is a relationship defined between rings that preserves many ring-theoretic properties. More precisely, two rings R, S are Morita equivalent (denoted by R ≈ S {\displaystyle R\approx S} ) if their categories of modules are additively equivalent (denoted by R M ≈ S M {\displaystyle {}_{R}M\approx {}_{S}M} ). It is…

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Overview

Motivation

Definition

Examples

Criteria for equivalence

Properties preserved by equivalence

Further directions

Significance in K-theory

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Map overview Semantic statistics

Morita equivalence

Nodes89
Edges88
Triples28
Avg. degree1.98
Density0.022472
Components1

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Morita equivalence

Top relations

related to Properties preserved by equivalence · 10
Morita equivalence → Artinian, Examples, For, Generally, Many, Morita, Noetherian, Properties, R-Mod, S-Mod
related to Motivation · 6
Morita equivalence → Because, Every, Morita, R-module, Rings, This
related to Significance in K-theory · 6
Morita equivalence → If, K-groups, K-theory, Morita, Quillen's, Since
related to Further directions · 5
Morita equivalence → Dual, In, Morita, Perhaps, This
is a · 1
Morita equivalence → relationship defined between rings that preserves many ring-theoretic properties

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Important terminology

morita equivalent rings equivalence modules ring displaystyle isomorphic functor properties category module defined preserved two left mn categories projective since

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Morita equivalenceis arelationship defined between rings that preserves many ring-theoretic properties0.90text
Morita equivalencerelated to Further directionsDual0.60section
Morita equivalencerelated to Further directionsThis0.60section
Morita equivalencerelated to Further directionsIn0.60section
Morita equivalencerelated to Further directionsPerhaps0.60section
Morita equivalencerelated to Further directionsMorita0.60section
Morita equivalencerelated to MotivationRings0.60section
Morita equivalencerelated to MotivationEvery0.60section
Morita equivalencerelated to MotivationR-module0.60section
Morita equivalencerelated to MotivationBecause0.60section
Morita equivalencerelated to MotivationMorita0.60section
Morita equivalencerelated to MotivationThis0.60section

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    Researching Morita equivalence? Use this map to explore Properties preserved by equivalence, Criteria for equivalence & Further directions and other closely related topics, then follow useful entities and relationships into deeper research. Automatically generated connections are research leads, so verify important facts in reliable sources.