Difference between revisions of "Inverse semigroup"

From Groupprops
Jump to: navigation, search
(New page: {{variation of|group}} {{semigroup property}} ==Definition== ===Symbol-free definition=== An '''inverse semigroup''' is a semigroup (i.e., a set with an associative binary operation...)
 
Line 18: Line 18:
 
===Weaker properties===
 
===Weaker properties===
 
* [[Stronger than::Regular semigroup]]
 
* [[Stronger than::Regular semigroup]]
 +
 +
==External links==
 +
 +
* {{planetmath-defined|InverseSemigroup}}

Revision as of 21:28, 4 July 2008

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

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 (S,*) is termed an inverse semigroup if for every a \in S, there is a unique c \in S satisfying the conditions aca = a and cac = c.

Relation with other properties

Stronger properties

Weaker properties

External links