Completely regular semigroup: Difference between revisions
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===Weaker properties=== | ===Weaker properties=== | ||
* [[Stronger than::Regular semigroup]] | * [[Stronger than::Regular semigroup]] | ||
* [[Stronger than::Epigroup]] | |||
===Incomparable properties=== | ===Incomparable properties=== | ||
Revision as of 21:37, 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
A completely regular semigroup is a semigroup (i.e., a set with associative binary operation) where the subsemigroup generated by any element is a group under the induced multiplication.
Note that the identity elements for these groups need not, in general, coincide. If they do coincide, then the completely regular semigroup is a group.