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- Trivial_semigroup abstract "In mathematics, a trivial semigroup (a semigroup with one element) is a semigroup for which the cardinality of the underlying set is one. The number of distinct nonisomorphic semigroups with one element is one. If S = { a } is a semigroup with one element then the Cayley table of S is as given below:The only element in S is the zero element 0 of S and is also the identity element 1 of S. However not all semigroup theorists consider the unique element in a semigroup with one element as the zero element of the semigroup. They define zero elements only in semigroups having at least two elements.In spite of its extreme triviality, the semigroup with one element is important in many situations. It is the starting point for understanding the structure of semigroups. It serves as a counterexample in illuminating many situations. For example, the semigroup with one element is the only semigroup in which 0 = 1, that is, the zero element and the identity element are equal. Further, if S is a semigroup with one element, the semigroup obtained by adjoining an identity element to S is isomorphic to the semigroup obtained by adjoining a zero element to S.The semigroup with one element is also a group.In the language of category theory, any semigroup with one element is a terminal object in the category of semigroups.".
- Trivial_semigroup wikiPageID "22757436".
- Trivial_semigroup wikiPageRevisionID "491586031".
- Trivial_semigroup hasPhotoCollection Trivial_semigroup.
- Trivial_semigroup subject Category:Algebraic_structures.
- Trivial_semigroup subject Category:Semigroup_theory.
- Trivial_semigroup type AlgebraicStructures.
- Trivial_semigroup type Artifact100021939.
- Trivial_semigroup type Object100002684.
- Trivial_semigroup type PhysicalEntity100001930.
- Trivial_semigroup type Structure104341686.
- Trivial_semigroup type Whole100003553.
- Trivial_semigroup type YagoGeoEntity.
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- Trivial_semigroup comment "In mathematics, a trivial semigroup (a semigroup with one element) is a semigroup for which the cardinality of the underlying set is one. The number of distinct nonisomorphic semigroups with one element is one. If S = { a } is a semigroup with one element then the Cayley table of S is as given below:The only element in S is the zero element 0 of S and is also the identity element 1 of S.".
- Trivial_semigroup label "Trivial semigroup".
- Trivial_semigroup sameAs m.05zz60f.
- Trivial_semigroup sameAs Q7844663.
- Trivial_semigroup sameAs Q7844663.
- Trivial_semigroup sameAs Trivial_semigroup.
- Trivial_semigroup wasDerivedFrom Trivial_semigroup?oldid=491586031.
- Trivial_semigroup isPrimaryTopicOf Trivial_semigroup.