Regular semigroup
From Groupprops
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 PHRASES: semigroup with all elements regular, regular being a weak version of invertible
Contents
Definition
Symbol-free definition
A regular semigroup is a semigroup (i.e., a set with associative binary operation) in which every element is regular.
Definition with symbols
A semigroup is termed a regular semigroup if every
is regular, i.e.:
- For every
, there exists a
such that
- Equivalently, for every
, there exists a
such that
and
.