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Uniform module: Uniform dimension of a module, Hollow modules and co-uniform dimension & Textbooks

In abstract algebra, a module is called a uniform module if the intersection of any two nonzero submodules is nonzero. This is equivalent to saying that every nonzero submodule of M is an essential submodule. A ring may be called a right (left) uniform ring if it is uniform as a right (left) module over itself.

Language: English [EN]
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Uniform module topic overview

The analysis highlights Uniform dimension of a module, Hollow modules and co-uniform dimension and Textbooks as prominent areas in the source structure around Uniform module.

Related topics
33
Source areas
6
Connected nodes
39
Extracted relationships
22
Concept neighborhoods
30
Bridge connections
39

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.

Overview · 11 topics
Uniform dimension of a module · 8 topics
Hollow modules and co-uniform dimension · 5 topics
Textbooks · 5 topics
Primary sources · 3 topics
Properties and examples of uniform modules · 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

Properties and examples of uniform modules

Uniform dimension of a module

Hollow modules and co-uniform dimension

Textbooks

Primary sources

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 Uniform module connects Entity context

The extracted context around Uniform module shows recurring relationship patterns in the source. For example, Uniform module → Equivalently, Fleury, Goldie, Grezeszcuk, Grzeszczuk, Miyashita, N1, N2, Puczylowski, Reiter, Reiter's, Studies, Takeuchi, The, These, Varadarajan Another extracted example is Uniform module → Any, Being, If N1, N2, The, Uniserial. Use these groups to spot repeated connection types before inspecting the individual relationships.

Uniform module

Top relations

related to Hollow modules and co-uniform dimension · 16
Uniform module → Equivalently, Fleury, Goldie, Grezeszcuk, Grzeszczuk, Miyashita, N1, N2, Puczylowski, Reiter, Reiter's, Studies, Takeuchi, The, These, Varadarajan
related to Properties and examples of uniform modules · 6
Uniform module → Any, Being, If N1, N2, The, Uniserial

Important terminology

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

Important terminology

dimension uniform module modules finite goldie hollow submodules dual doi ring dim right also mr semisimple 10 submodule theorem rings

Uniform module relationships Subject–Predicate–Object triples

TTTA extracted 22 structured relationships around Uniform module. Examples in this analysis include Uniform module → related to Hollow modules and co-uniform dimension → The and Uniform module → related to Hollow modules and co-uniform dimension → N1. The table shows each extracted connection, where it came from and its confidence.

SubjectPredicateObjectConfidenceSrc
Uniform modulerelated to Hollow modules and co-uniform dimensionThe0.60section
Uniform modulerelated to Hollow modules and co-uniform dimensionN10.60section
Uniform modulerelated to Hollow modules and co-uniform dimensionN20.60section
Uniform modulerelated to Hollow modules and co-uniform dimensionEquivalently0.60section
Uniform modulerelated to Hollow modules and co-uniform dimensionThese0.60section
Uniform modulerelated to Hollow modules and co-uniform dimensionGoldie0.60section
Uniform modulerelated to Hollow modules and co-uniform dimensionStudies0.60section
Uniform modulerelated to Hollow modules and co-uniform dimensionFleury0.60section
Uniform modulerelated to Hollow modules and co-uniform dimensionReiter0.60section
Uniform modulerelated to Hollow modules and co-uniform dimensionTakeuchi0.60section
Uniform modulerelated to Hollow modules and co-uniform dimensionVaradarajan0.60section
Uniform modulerelated to Hollow modules and co-uniform dimensionMiyashita0.60section

Related concept clusters Concept neighborhoods

The concept neighborhoods around Uniform module bring nearby vocabulary together. In this analysis, examples include Dimension, Module and Uniform. Use the clusters to find adjacent concepts and terminology that may deserve separate research.

  • Uniform module
    • Dimension
    • Module
    • Uniform
    • Submodules
    • Modules
    • Ring
    • Finite
    • Displaystyle
    • Goldie
    • Notion
    • Two
    • Right
  • uniform module
    • Dimension
    • Module
    • Uniform
    • Submodules
    • Modules
    • Displaystyle
    • Finite
    • Ring
    • Hollow
    • Notion
    • Goldie
    • Right
  • alfred goldie
    • Dual
    • Mr
    • Doi
    • Dimension
    • Issn
    • Notion
    • Theorem
    • Modules
    • Uniform
    • Also
    • Right
    • Module
  • dimension
    • Uniform
    • Hollow
    • Finite
    • Modules
    • Module
    • Goldie
    • Artinian
    • Varadarajan
    • Semisimple
    • Also
    • Dual
    • Rings
  • dimension of a vector space
    • Uniform
    • Hollow
    • Finite
    • Modules
    • Module
    • Goldie
    • Artinian
    • Varadarajan
    • Semisimple
    • Also
    • Dual
    • Rings
  • artinian modules
    • Semisimple
    • Noetherian
    • Uniform
    • Finite
    • Co-uniform
    • Varadarajan
    • Direct
    • Hollow
    • Dual
    • Dimension
    • Contains
    • Sum
  • noetherian modules
    • Uniform
    • Co-uniform
    • Direct
    • Domain
    • Dual
    • Contains
    • Sum
    • Submodules
    • Hollow
    • Issn
    • Semisimple
    • Doi
  • uniserial modules
    • Uniform
    • Co-uniform
    • Direct
    • Dual
    • Contains
    • Sum
    • Submodules
    • Hollow
    • Issn
    • Doi
    • Varadarajan
    • Also

Connections between topic areas Semantic bridges

For Uniform module, one of the stronger structural bridges in this analysis connects Uniform module with Overview. 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
Uniform module — Overview · splits 28 ⟂ 12
Uniform module — Uniform dimension of a module · splits 31 ⟂ 9
Uniform module — Hollow modules and co-uniform dimension · splits 34 ⟂ 6
Uniform module — Textbooks · splits 34 ⟂ 6
Uniform module — Primary sources · splits 36 ⟂ 4

Map overview Semantic statistics

Uniform module

Nodes40
Edges39
Triples22
Avg. degree1.95
Density0.05
Components1

Source & methodology

TTTA analyzes the structure around Uniform module to surface related topics, entities, relationships, concept neighborhoods and bridge connections. Use the map to explore areas such as Uniform dimension of a module, Hollow modules and co-uniform dimension & Textbooks, including less central topics that may reveal useful research gaps. Automatically extracted connections are research leads rather than rewritten encyclopedia content.

Source: Wikipedia — Uniform module · EN edition · Analysis: TopicsToTalkAbout

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