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Graded ring

In mathematics, in particular abstract algebra, a graded ring is a ring such that the underlying additive group is a direct sum of abelian groups R i {\displaystyle R_{i}} such that ⁠ R i R j ⊆ R i + j {\displaystyle R_{i}R_{j}\subseteq R_{i+j}} ⁠. The index set is usually the set of nonnegative integers or the set of integers, but can be any monoid. The…

Art, Basic examples & Graded module

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Overview

First properties

Basic examples

Graded module

Invariants of graded modules

Graded algebra

G-graded rings and algebras

Graded monoid

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Map overview Semantic statistics

Graded ring

Nodes95
Edges94
Triples33
Avg. degree1.98
Density0.021053
Components1

How this topic connects Entity context

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Graded ring

Top relations

related to Basic examples · 6
Graded ring → Any, If, Let, The, Then, This
related to Anticommutativity · 5
Graded ring → An, Gamma, Some, Specifically, This
related to Graded monoid · 5
Graded ring → Formally, Intuitively, Note, Some, That
is a · 4
Graded ring → graded module over itself, ring A graded with respect to Γ, ring such that the underlying additive group is a direct sum of abelian groups R i, ring that is decomposed into a direct sum R
related to Invariants of graded modules · 4
Graded ring → Given, Hilbert, It, Poincaré
related to First properties · 2
Graded ring → Generally, This
related to G-graded rings and algebras · 2
Graded ring → G-graded, The
related to Quotients · 2
Graded ring → If, R/I
see also · 2
Graded ring → Associated, Graded
related to Graded module · 1
Graded ring → The

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Important terminology

graded displaystyle ring module monoid homogeneous algebra degree mathbb elements sum direct also ideal gradation called algebras set modules element

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Graded ringis aring such that the underlying additive group is a direct sum of abelian groups R i0.90text
Graded ringis aring that is decomposed into a direct sum R0.90text
Graded ringis agraded module over itself0.90text
Graded ringis aring A graded with respect to Γ0.90text
Graded ringrelated to AnticommutativitySome0.60section
Graded ringrelated to AnticommutativityThis0.60section
Graded ringrelated to AnticommutativitySpecifically0.60section
Graded ringrelated to AnticommutativityGamma0.60section
Graded ringrelated to AnticommutativityAn0.60section
Graded ringrelated to Basic examplesAny0.60section
Graded ringrelated to Basic examplesThis0.60section
Graded ringrelated to Basic examplesThe0.60section

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