# Difference between revisions of "Inverse semigroup"

From Groupprops

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{{variation of|group}} | {{variation of|group}} | ||

{{semigroup property}} | {{semigroup property}} | ||

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==Definition== | ==Definition== | ||

## Revision as of 22:18, 24 June 2012

This is a variation of group|Find other variations of group | Read a survey article on varying group

This article defines a semigroup property: a property that can be evaluated to true/false for any given semigroup

View a complete list of semigroup properties

{{quick phrase|[[quick phrase::semigroup where every element has a unique *inverse* in the semigroup sense (i.e., without reference to neutral elements)}}

## Contents

## Definition

### Symbol-free definition

An **inverse semigroup** is a semigroup (i.e., a set with an associative binary operation) where every element has a unique inverse in the semigroup sense.

### Definition with symbols

A semigroup is termed an **inverse semigroup** if for every , there is a unique satisfying the conditions and .