Regular semigroup: Difference between revisions
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{{variation of|group}} | {{variation of|group}} | ||
{{semigroup property}} | {{semigroup property}} | ||
{{quick phrase|[[quick phrase::semigroup with all elements regular, regular being a weak version of invertible]]}} | |||
==Definition== | ==Definition== | ||
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* [[Weaker than::Group]] | * [[Weaker than::Group]] | ||
* [[Weaker than::Clifford semigroup]] | |||
* [[Weaker than::Completely regular semigroup]] | |||
* [[Weaker than::Inverse semigroup]] | * [[Weaker than::Inverse semigroup]] | ||
Latest revision as of 22:16, 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 PHRASES: semigroup with all elements regular, regular being a weak version of invertible
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 .