Inverse semigroup

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This article defines a semigroup property: a property that can be evaluated to true/false for any given semigroup
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QUICK PHRASES: semigroup where every element has a unique inverse in the semigroup sense (i.e., without reference to neutral elements)

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