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Associated prime: Properties, Examples & Overview

In abstract algebra, an associated prime of a module M over a ring R is a type of prime ideal of R that arises as an annihilator of a (prime) submodule of M. The set of associated primes is usually denoted by Ass R ⁡ ( M ) , {\displaystyle \operatorname {Ass} _{R}(M),} and sometimes called the assassin or assassinator of M (word play between the notation…

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Associated prime topic overview

The analysis highlights Properties, Examples and Overview as prominent areas in the source structure around Associated prime.

Related topics
27
Source areas
4
Connected nodes
31
Extracted relationships
22
Concept neighborhoods
24
Bridge connections
31

What this topic covers Research coverage

Source areas are shown by the number of related topics found in each part of the analysis. Use smaller areas too: they can reveal specialized angles and content gaps.

Properties · 12 topics
Overview · 11 topics
Examples · 3 topics
Definitions · 1 topics

Smaller areas are not necessarily less important. They contain fewer connections in this analysis and can be useful for finding specialized angles or coverage gaps.

Explore all related topics Closing gaps

Browse the complete topic structure, not only the most central items. Less prominent entities and concepts can reveal missing angles, specialized context and useful research gaps. Each item opens a new analysis centered on that subject.

Overview

Definitions

Properties

Examples

Advanced semantic analysis

Deeper signals for content research, entity SEO and topical coverage. The plain-language headings explain what each technical view is useful for.

How Associated prime connects Entity context

The extracted context around Associated prime shows recurring relationship patterns in the source. For example, Associated prime → Any, Artinian, Ass, For, However, If, It, Lam, Matlis' Theorem, Moreover, Most, Noetherian, Spec Another extracted example is Associated prime → An, Ann, For, In, R-module, R/P. Use these groups to spot repeated connection types before inspecting the individual relationships.

Associated prime

Top relations

related to Properties · 13
Associated prime → Any, Artinian, Ass, For, However, If, It, Lam, Matlis' Theorem, Moreover, Most, Noetherian, Spec
related to Definitions · 6
Associated prime → An, Ann, For, In, R-module, R/P
related to Examples · 2
Associated prime → If, The
is a · 1
Associated prime → annihilator

Important terminology

Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.

Important terminology

associated displaystyle prime primes ring module ideal commutative ass noetherian submodule algebra set ideals mathrm called operatorname primary annihilator nonzero

Associated prime relationships Subject–Predicate–Object triples

TTTA extracted 22 structured relationships around Associated prime. Examples in this analysis include Associated prime → is a → annihilator and Associated prime → related to Definitions → R-module. The table shows each extracted connection, where it came from and its confidence.

SubjectPredicateObjectConfidenceSrc
Associated primeis aannihilator0.90text
Associated primerelated to DefinitionsR-module0.60section
Associated primerelated to DefinitionsAnn0.60section
Associated primerelated to DefinitionsFor0.60section
Associated primerelated to DefinitionsAn0.60section
Associated primerelated to DefinitionsIn0.60section
Associated primerelated to DefinitionsR/P0.60section
Associated primerelated to ExamplesIf0.60section
Associated primerelated to ExamplesThe0.60section
Associated primerelated to PropertiesMost0.60section
Associated primerelated to PropertiesLam0.60section
Associated primerelated to PropertiesIf0.60section

Related concept clusters Concept neighborhoods

The concept neighborhoods around Associated prime bring nearby vocabulary together. In this analysis, examples include Primes, Prime and Ring. Use the clusters to find adjacent concepts and terminology that may deserve separate research.

  • Associated prime
    • Primes
    • Prime
    • Ring
    • Module
    • Ann
    • Displaystyle
    • Commutative
    • Ideal
    • Noetherian
    • Ass
    • Ideals
    • Submodule
  • associated prime
    • Primes
    • Displaystyle
    • Ideal
    • Prime
    • Ring
    • Module
    • Ann
    • Ideals
    • Nonzero
    • Commutative
    • Mathrm
    • Submodule
  • ring
    • Noetherian
    • Finitely
    • Commutative
    • Primes
    • Spectrum
    • Classes
    • Injective
    • Integers
    • One
    • Order
    • Modules
    • Coprimary
  • prime ideals
    • Displaystyle
    • Ideal
    • Linked
    • Ann
    • Ideals
    • Nonzero
    • Prime
    • Mathrm
    • Primary
    • Submodule
    • Set
    • Ring
  • commutative algebra
    • Commutative
    • Mathematics
    • Noetherian
    • Primes
    • Ring
    • Decomposition
    • Submodule
    • Finitely
    • Ideal
    • Rings
    • Primary
    • Linked
  • commutative
    • Noetherian
    • Primes
    • Ring
    • Decomposition
    • Finitely
    • Mathematics
    • Rings
    • Primary
    • Nonzero
    • Module
    • Prime
    • Also
  • local ring
    • Noetherian
    • Finitely
    • Commutative
    • Primes
    • Spectrum
    • Classes
    • Injective
    • Integers
    • One
    • Order
    • Modules
    • Coprimary
  • artinian ring
    • Noetherian
    • Finitely
    • Commutative
    • Primes
    • Spectrum
    • Classes
    • Injective
    • Integers
    • One
    • Order
    • Modules
    • Coprimary

Connections between topic areas Semantic bridges

For Associated prime, one of the stronger structural bridges in this analysis connects Associated prime with Properties. Bridges highlight paths between different parts of the map and can reveal research angles that are easy to miss in a flat list.

Min side: 3
Associated prime — Properties · splits 19 ⟂ 13
Associated prime — Overview · splits 20 ⟂ 12
Associated prime — Examples · splits 28 ⟂ 4

Map overview Semantic statistics

Associated prime

Nodes32
Edges31
Triples22
Avg. degree1.94
Density0.0625
Components1

Source & methodology

TTTA analyzes the structure around Associated prime to surface related topics, entities, relationships, concept neighborhoods and bridge connections. Use the map to explore areas such as Properties, Examples & Overview, including less central topics that may reveal useful research gaps. Automatically extracted connections are research leads rather than rewritten encyclopedia content.

Source: Wikipedia — Associated prime · EN edition · Analysis: TopicsToTalkAbout

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