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Perfect ring

In the area of abstract algebra known as ring theory, a left perfect ring is a type of ring over which all left modules have projective covers. The right case is defined by analogy, and the condition is not left-right symmetric; that is, there exist rings which are perfect on one side but not the other. Perfect rings were introduced in Bass's book.

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Perfect ring

SemisimpleJacobson radicalDescending chain conditionPrincipal right idealsFlat
16 related topics

Semiperfect ring

SimpleCategoryKrull-Schmidt
3 related topics

Examples

Finite dimensionalAlgebras
2 related topics

Properties

Morita equivalent
1 related topics

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Overview

Perfect ring

Examples

Properties

Semiperfect ring

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Map overview Semantic statistics

Perfect ring

Nodes35
Edges34
Triples30
Avg. degree1.94
Density0.057143
Components1

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Perfect ring

Top relations

related to Definitions · 10
Perfect ring → Anderson, Bass' Theorem, Every, Fuller, Jacobson, R-module, R/J, T-nilpotent, The, There
related to Properties · 8
Perfect ring → An, Baer's, For, From, Morita, R-module, R-modules, Since
related to Basic ring · 6
Perfect ring → EndR, For, Given, Morita, R/J, The
related to Examples · 5
Perfect ring → Artinian, Examples, Finite, Left, Local
is a · 1
Perfect ring → type of ring over which all left modules have projective covers

Important terminology Word statistics

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Important terminology

ring projective left perfect right every rings semiperfect r-module cover modules idempotents equivalent ideals finitely generated basic local condition left-right

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Perfect ringis atype of ring over which all left modules have projective covers0.90text
Perfect ringrelated to Basic ringFor0.60section
Perfect ringrelated to Basic ringMorita0.60section
Perfect ringrelated to Basic ringR/J0.60section
Perfect ringrelated to Basic ringGiven0.60section
Perfect ringrelated to Basic ringThe0.60section
Perfect ringrelated to Basic ringEndR0.60section
Perfect ringrelated to DefinitionsThe0.60section
Perfect ringrelated to DefinitionsAnderson0.60section
Perfect ringrelated to DefinitionsFuller0.60section
Perfect ringrelated to DefinitionsEvery0.60section
Perfect ringrelated to DefinitionsR-module0.60section

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