Research any topic before you write.

Find related topics. | Discover entities. | See connections. | Build a topical map.

Regular semigroup

In mathematics, a regular semigroup is a semigroup S in which every element is regular, i.e., for each element a in S there exists an element x in S such that axa = a. Regular semigroups are one of the most-studied classes of semigroups, and their structure is particularly amenable to study via Green's relations.

History & Art

Use the mouse wheel or two fingers (on touchscreens) to zoom in and out of the map.

Research this topic

Explore the main themes, entities and connections around Regular semigroup. Start with the topic map, then use the sections below for research and deeper semantic analysis.

Explore this topic

Start with a few of the strongest sections from the source topic. These are research directions, not a list of keywords you must use.

Topics to explore

Browse the full topic structure. Each item opens a new analysis centered on that subject.

Overview

History

The basics

Green's relations

Special classes of regular semigroups

Generalizations

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.

Map overview Semantic statistics

Regular semigroup

Nodes46
Edges45
Triples35
Avg. degree1.96
Density0.043478
Components1

How this topic connects Entity context

See the strongest relationship patterns around the current topic before diving into the raw triples.

Regular semigroup

Top relations

related to history · 13
Regular semigroup → According, David Rees, French, Gabriel Thierrin, Green, Green's, It, John, Neumann, On, Paul Dubreil, Regular, The
related to Green's relations · 5
Regular semigroup → Green's, If, In, Recall, S1
related to Examples of regular semigroups · 4
Regular semigroup → Any, Every, Rees, The
related to Special classes of regular semigroups · 4
Regular semigroup → Generalised, Locally, Orthodox, Some
related to The basics · 4
Regular semigroup → Conversely, Then, There, To
related to Unique inverses and unique pseudoinverses · 3
Regular semigroup → Suppose, Then, To
is a · 1
Regular semigroup → semigroup S in which every element is regular
related to Generalizations · 1
Regular semigroup → E-inversive

Important terminology Word statistics

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

Important terminology

semigroup regular semigroups inverse element every unique idempotents relations green's idempotent classes one inverses mathematics displaystyle mathcal axa structure isbn

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Regular semigroupis asemigroup S in which every element is regular0.90text
Regular semigrouprelated to Examples of regular semigroupsEvery0.60section
Regular semigrouprelated to Examples of regular semigroupsThe0.60section
Regular semigrouprelated to Examples of regular semigroupsAny0.60section
Regular semigrouprelated to Examples of regular semigroupsRees0.60section
Regular semigrouprelated to GeneralizationsE-inversive0.60section
Regular semigrouprelated to Green's relationsRecall0.60section
Regular semigrouprelated to Green's relationsS10.60section
Regular semigrouprelated to Green's relationsIn0.60section
Regular semigrouprelated to Green's relationsGreen's0.60section
Regular semigrouprelated to Green's relationsIf0.60section
Regular semigrouprelated to historyRegular0.60section

Related concept clusters Concept neighborhoods

These clusters group vocabulary that occurs around closely connected concepts in the source material.

    Connections between topic areas Semantic bridges

    Bridges can reveal useful research angles that are easy to miss in a flat list of related terms.

    Min side: 3
    For writers, content strategists, SEOs, marketers and creators — from quick topic research to advanced semantic analysis.